Pius W Akumbu

Esther P Chie

Multilingualism among the Mbororo of the North-West Region of Cameroon An Overview

This study examines the languages used by the Mbororo living in Badem, Kejom Ketinguh (Babanki Tungo), in the North-West Region of Cameroon, to shed light on the factors responsible for their multilingualism. 1 The North-West Region has been recognized as one of the country's most linguistically heterogenous regions (Eberhard, Simons, and Fennig 2019), with about a hundred languages spoken by around two million people in a total surface area of 17,812 square kilometers (UCCC 2014). Many people in this region, like in the rest of English-speaking Cameroon, are multilingual in their mother tongue, Cameroon Pidgin English (CPE), and at least one other language. The seminomadic Mbororo cattle-rearers dispersed throughout the region are highly multilingual, but no study thus far has sought to understand the conditions of their multilingualism.

Observations, questionnaires, and discussions with speakers reveal that most of the Mbororo in Badem above six years of age are multilingual in at least Fulfulde, CPE, and Babanki, the indigenous language of Kejom Ketinguh. The Mbororo hold a language ideology where Fulfulde is "primary" and other languages are learned for specific purposes (integration, grazing, trade, travel, etc.); for this reason, their children are monolingual during their early years before they begin to acquire other languages.

This study begins with some historical information on the migration of the Mbororo and the methods used to collect data. The languages used by the Mbororo are presented in section 2, while the conditions of their multilingualism are discussed in section 3. In section 4, we attempt to draw lessons from

the situation of the Mbororo for the understanding of rural multilingualism in Cameroon, before summarizing the conclusions in section 5.

Historical Background

The Mbororo are a pastoralist people who live in at least twenty-three countries across Africa. 2 [START_REF] Amadou | The Mbororo Problem in North West Cameroon: A Historical Investigation[END_REF] reports that the Mbororo began to enter the Cameroonian Grassfields in the 1910s, driven by their continuous search for pastureland. They left northern Nigeria in the early nineteenth century, slowly migrating to the east and the south. Their movements were guided by ecological and political considerations, with the central goal of sustaining their pastoral economy. Because the western Grassfields provided exceptionally favorable conditions that promoted the growth of their herds, many families settled in this area. The Mbororo live in an isolated way in small remote communities and have frequently come into conflict with their majority host communities, who despise them as illegal immigrants or land-grabbing invaders. This has resulted in conflicts between the indigenous farmers and the Mbororo graziers, which in some cases have led to exploitation, oppression, harassment, and humiliation of Mbororo people.

The village of Kejom Ketinguh (see figure 1.1) was originally inhabited only by the Babanki. In 1916, it witnessed the arrival of some thirty Fulfulde-speaking Mbororo families under the leadership of Ardo Sabga. They settled in one of the quarters of Kejom Ketinguh, along the ring road that was later named Sabga after the ardo. In 1940, some of the families moved to the more hilly outskirts of Kejom Ketinguh, settling in Badem, but they left in 1958 because of disputes over grazing land. They returned in 1970 to their present site but continued to perceive themselves as politically marginalized. The hostilities that prevailed between the two communities have dwindled over the last four decades, to the extent that the Mbororo now interact with the Babanki more closely and are generally considered to be part of the Kejom Ketinguh community. Many of them now own land and construct permanent houses for their families. It is even the case that one Mbororo was appointed as a member of the Kejom Ketinguh village traditional council in 2010 (Issa Bouba, personal communication).

Data Collection

In March 2017, the researchers spent two days in Badem, Kejom Ketinguh, administering questionnaires, to find out which languages the Mbororo use and the reasons why they use several different languages. The first author was born and raised in Badem, and he developed close ties with the Mbororo and interacted constantly with them until the age of thirteen when he left the area to attend secondary school. This relationship facilitated the data collection process-ordinarily, the Mbororo are highly reserved and would not easily agree to reveal information about themselves.

Of the community of approximately 200 inhabitants, 47 people-20 females and 27 males-participated in our study (see table 1.1 for a summary of the sex, age, and educational level of participants). In addition to responding to the specific questions we asked, the consultants usually stayed behind after answering the questionnaire, and we continued talking with them and hearing more about their experiences with the languages they spoke. We also had the opportunity to observe interactions between the Mbororo and some Babanki who happened to be in the area when we visited.

During the two days of data collection, we spoke both CPE and Babanki. We explained to the participants that the data we collected were to be used only for academic purposes to help us understand the languages that people use and why they learn several languages. Most of the respondents were unable to write (because they lack any formal education), and so we read out the questions and wrote down the responses that they gave us.

LANGUAGE DIVERSITY

Based on the responses to the questionnaires, at least twenty languages were used by the forty-seven Mbororo consultants with whom we worked. 3 There were four monolingual participants who could speak only Fulfulde; however, they were all aged five or below. A further seven participants could speak only three languages: in all cases, these were Fulfulde, CPE, and Babanki. Of these seven, four were aged between six and ten years, while the three others were women aged forty-one or older. The remaining thirty-six respondents, a large majority, use at least four languages. Indeed, four of them reported using more than ten languages, and one participant listed thirteen languages that he could understand.

Before looking in more detail at some of the languages and why they are spoken, it is worth noting, based purely on the data presented thus far, that age, sex, and level of education are all factors that affect the number of languages spoken by a member of the Mbororo community of Badem. In addition to their mother tongue, the Mbororo learn CPE and Babanki when they are approximately five to seven years old, with other languages learned after that. Since most Mbororo people speak more CPE than Babanki, we assume that CPE is learned before Babanki.

Cameroon Pidgin English

CPE is an English-lexified pidgin/creole spoken, in some form, by at least half of Cameroon's population. It is the major lingua franca, especially in the anglophone regions but also in urban centers throughout the country. A wide range of names are used for the language-Eberhard, Simons, and Fennig (2019) list Cameroon Creole, Cameroon Creole English, Cameroonian Creole, Kamtok, Wes Cos, and "Bush English" as alternatives. Kamtok has become one of the most widely used names, and Todd, Jumbam, and Wamey (n.d.) consider that there are up to five varieties, which they refer to as Grafi Kamtok (spoken in the North-West Region), liturgical Kamtok, francophone Kamtok, Limbe Kamtok, and Bororo Kamtok (the variety spoken by the Mbororo in our study).

CPE is a broadly dispersed language, and is spoken by both the Babanki and the Mbororo. Unless a Mbororo has learned Babanki, CPE is, generally speaking, the only language he or she can use to communicate with a Babanki. Thus, a Babanki would first speak CPE to a Mbororo who is not known to speak Babanki. If, however, the Mbororo knows Babanki, they would then continue the conversation in that language.

CPE is the language the Mbororo learn first after acquiring Fulfulde. In our data, all participants above the age of five were able to communicate in CPE.

Babanki

Babanki is the language of the host community of the Mbororo of Badem. It is a Central Ring Grassfields Bantu language spoken by approximately 39,000 people, mainly in the two settlements of Kejom Ketinguh or Babanki Tungo and Kejom Keku or Big Babanki (Eberhard, Simons, and Fennig 2019;[START_REF] Hammarström | Max Planck Institute for the Science of Human History[END_REF], but also to some extent in diaspora communities.

Those Mbororo who have learned Babanki use it when in contact with the Babanki people of Kejom Ketinguh. They consider that speaking Babanki facilitates their belonging in the community and enables them to achieve certain goals, such as hiring labor from the Babanki to work in their farms or to tend their cattle. Using Babanki also helps the Mbororo to more easily receive support from the Babanki when needed-for example, if their cattle are stolen, the Babanki can join forces with them to look for the thieves. In the event of conflict between members of the Mbororo and the Babanki, Babanki is used to negotiate, particularly when it is a member of the Mbororo that is at fault. Thus, one can say that the Babanki language serves as a uniting factor, facilitating the integration of the minority Mbororo into their host community.

All the participants aged between six and forty years claimed to speak Babanki, and we confirmed this by chatting with them in that language.

Other Languages

Apart from Fulfulde, CPE, and Babanki, seventeen other languages were reported as being used by the Mbororo who participated in our study. These languages fall into a number of different types. Firstly, English is used as the language of instruction in school and French is a school subject, and consequently those participants who had been to school were familiar with these two languages. 4 Secondly, Hausa, Arabic, and Bamun are languages that are used regionally in relation to Islam, and thus some Mbororo had learned them by associating with other Muslims. Thirdly, Pinyin, Bambili, Noni, Bafut, Lamnso, and Awing had been learned by those Mbororo that had lived for extended periods of time in areas where those languages are spoken. Finally, Kenswei Nsei, Vengo, Bamali, Bamunka, Nyong, and Bambalang had been learned by some of the men and boys when they moved in the dry season with their cattle to these neighboring lowland communities where there was green pasture. Many of these languages had also been learned as a result of contact with other speakers during cattle-trading. While this gives the bare outline of the reasons for the range of languages that are spoken by the participants, in the following section we consider the reasons for multilingualism as advanced by the consultants themselves.

MOTIVATIONS FOR MULTILINGUALISM

As has been noted, multilingualism among the Mbororo of Badem is the norm, and begins around the age of six. Before this age, children are monolingual in Fulfulde, and as they begin to interact with the broader community of Kejom Ketinguh they learn both CPE and Babanki. All participants who had attended school said they spoke English, while a few who had attended secondary school said they understood a bit of French. However, as we have seen, the participants reported using many other languages. Some reasons advanced by the participants themselves for this expansive multilingualism are presented here.

Communication and Integration

Multilingualism is common in situations where communities who use different languages come into contact, because of the simple need for communication between human beings with different linguistic backgrounds. One of the ways in which such a situation can occur is population movement, where a group of immigrants comes into contact with the existing population of a particular location, who speak another language. In order to communicate, members of each group need to have at least some command of each other's language [START_REF] Edwards | Societal Multilingualism: Reality, Recognition and Response[END_REF]. The participants in this study made it clear that the primary reason they saw for multilingualism among the Mbororo is the simple need to communicate with the Babanki and become part of a community where they had found grazing land and where they wished to remain.

While the Mbororo aged forty or younger are mostly fluent in Babanki (except those below the age of six), the majority of participants older than forty are not fluent speakers of this language. That reflects the fact that as the Mbororo finally settled and were accepted as part of Kejom Ketinguh, Mbororo children could socialize with Babanki children and learn the language. A few of the older Mbororo can understand Babanki, but are unable to speak it. They noted that they did not learn it the way their children did because, in the past, the Mbororo had many problems with the Babanki, so they were unable to interact sufficiently to learn the language. As mentioned in section 1.1, over the last four decades, the Babanki have become more accommodating and have accepted the Mbororo as part of the community. This has made it possible for most of the Mbororo who are under the age of forty years to learn the language as soon as they begin interacting more extensively with the people of Kejom Ketinguh outside their own community.

The comments of the participants in our study reflect the need for Babanki to communicate and integrate into the local community. For example, one of the consultants, aged thirty-nine, said that they learned Babanki because "Dem born me for yah and I get for talk witi Babanke pipu" (I was born here and I need to communicate with Babanki people). Another, aged fourteen, said that "Nobi dem born me na for yah? Na ma kondri" (I was born here. It is my village). A sixty-year-old man noted, "Taim whe we kam for yah, we bi get for learn Babanke for sika say we bin wan place for sitop witi we kawu" (When we arrived here, we had to learn Babanki because we wanted grazing land).

The need to communicate with other people in Kejom Ketinguh and to integrate into the community is clearly the main driver for the Mbororo to learn Babanki, the language of their host community.

Grazing

As seminomadic cattle-rearers, the Mbororo move with their cattle during the dry season in search of green pasture. Kejom Ketinguh is in a hilly landscape, and the grass withers during the dry season, leaving the cattle with insufficient food. However, there are neighboring settlements in lowland areas with enough water to maintain green vegetation during the dry season, and so Mbororo men and boys move to such areas with their cattle and remain there throughout the dry season, which lasts approximately three months. During this time, they interact and communicate with members of those communities; in many cases, friendships and business networks are developed, making it possible for the Mbororo to return to those communities for visits or commercial activities.

All of this enables those Mbororos to learn the language of their temporary hosts. Twenty of the twenty-three male respondents above the age of ten could speak the language of one of the neighboring communities because they had been there with their cattle during a dry season; the other three could speak the languages of several other communities, because they had taken their cattle to different settlements in different years. The villages of the Ndop plain, which lies below Kejom Ketinguh to the southeast-Bamessing, Bamali, Balikumbat, Bambalang, and Babungo-are the most popular dry season hosts. All twenty-three boys and men aged above ten speak one or more of the languages of these villages.

A thirty-two-year-old male consultant summed up the experience of learning languages as a result of moving with his cattle during the dry season. As he put it, "Me a di talk plenti talk. If na you you go talk da pipu dem talk. You di stay de for teri moon, you de witi dem plenti taim" (I speak so many languages. If you do it, you will learn those languages too. You live there for three months and you are with them most of the time). [START_REF] Edwards | Societal Multilingualism: Reality, Recognition and Response[END_REF] points out that trade is one of the major reasons for multilingualism, and this is reflected in the experience of the Mbororo. The Mbororo depend on their cattle for their livelihood. Until recently, selling their cattle was the only way in which they were able to buy other basic needs such as food and household items. However, in the last two decades, they have been involved in farming-the main crops are beans, corn, and njamanjama 5 -hiring others from Kejom Ketinguh to cultivate their farms. Within the community, men are responsible for selling cattle and purchasing household items and clothing for the family, while women concentrate on household chores such as cooking and laundry.

Trade

A sixty-seven-year-old female participant reported that she spoke only Fulfulde, CPE, and a bit of Babanki. She said that for the forty-seven years since she got married and settled in Kejom Ketinguh in 1970, her place had been in the home. Her husband did not allow her or his other wife to go anywhere-if she left, it was to visit a relative for a specific reason (e.g., bereavement), and the only time she had gone to a market was when she was on the way to visit her sister and needed to buy something. She indicated that this explained her relative lack of multilingualism.

In contrast, many of the male consultants learned other languages while trading, often in the cattle markets. In the markets of the North-West Region, prices are not fixed, but bargained. Speaking the trader's language is one of the factors that influence the negotiations: the buyer is likely to get a better price if they bargain in the language of the seller. It is therefore to the advantage of the Mbororo men to speak as many languages as possible to enable them trade with speakers of different languages. As a seventy-one-year-old male participant said, "If you no know da talk dem go cheat you, dem go take you planti moni" (If you don't understand the language, you will be cheated and they will collect more money from you).

UNDERSTANDING RURAL MULTILINGUALISM

Early work on multilingualism in Cameroon and across Africa tended to focus on urban centers (e.g., [START_REF] Laughlin | Introduction to the Languages of Urban Africa[END_REF] while neglecting rural settings. Approaches to sociolinguistic studies and language documentation were also generally based on the mistaken notion that languages belong to and are spoken in specific villages or by specific tribes, and linguists sought to identify the ancestral code in each case. This left the impression that multilingualism was restricted to urban centers, whereas in fact rural multilingualism clearly existed before its urban counterpart was ushered in by colonization.

In recent years, however, the focus of such studies has often shifted to an examination of nonancestral codes (e.g., [START_REF] Childs | Beyond the Ancestral Code: Towards a Model for Sociolinguistic Language Documentation[END_REF]. Despite this, it seems that no study has yet attempted to understand the multilingual practices of the seminomadic Mbororo people, who do not have villages of their own but rather settle in remote areas in the outskirts of established villages, where they are considered "strangers" [START_REF] Brooks | Landlords and Strangers: Ecology, Society, and Trade in Western Africa[END_REF] or latecomers [START_REF] Kopytoff | The Internal African Frontier: The Making of African Political Culture[END_REF].

Many Cameroonians living in rural areas are multilingual, and for the Mbororo in the North-West Region, this involves controlling at least their mother tongue, CPE, and one or more indigenous languages-through the nature of their settlement pattern and their daily activities, the Mbororo have tended to learn the languages of their host and neighboring communities. Some who have been to school also understand English and French.

Multilingualism is conditioned by the language ideologies of speakers, that is "the cultural (or subcultural) system of ideas about social and linguistic relationships, together with their loading of moral and political interests" (Irvine 1989, 255). In the case of the Mbororo, based on the data collected for this study, they hold a language ideology where Fulfulde is "primary," and other languages are learned for specific purposes.

Multilingualism among the Mbororo is thus similar, in some ways, to that which is brought about by migration into urban centers and so is typical of the industrialized world [START_REF] García | The Multilingual Apple: Languages in New York City[END_REF]Extra and Yağmur 2004;Clyne andKipp 2006a, 2006b). The Mbororo brought Fulfulde with them to Kejom Ketinguh; they acquire CPE, which is the lingua franca of the North-West Region; they learn Babanki, the language of their host community; and they also pick up any other language with which they maintain contact.

This kind of multilingualism reflects what [START_REF] Moore | Multilingualism and Second Language Acquisition in the Northern Mandara Mountains[END_REF] has found among the Wandala of northern Cameroon. Like children among the Wandala, Mbororo children grow up in a largely monolingual world, and languages other than their traditional language, Fulfulde, are learned later in life. CPE is required for wider communication, Babanki for integration into the host village, English and French for educational purposes, Arabic for religious reasons, and other indigenous languages for the purposes of grazing, trade, and travel.

The situation described here for the Mbororo in Kejom Ketinguh, and indeed that in most rural areas of northwest Cameroon where the Mbororo are found, is slightly different from what Matras (2009, 48) describes for "rural border areas and ethnically mixed regions," where he says that "languages are acquired through face-to-face interaction [and] there is more frequently an equal incentive for people from all communities to acquire each other's languages." Instead, the multilingualism described here is largely unidirectional: while the Mbororo in Kejom Ketinguh learn Babanki, the Babanki do not learn Fulfulde; and more generally, the minority migrant Mbororo people mostly learn the languages of their host communities, rather than the indigenous peoples learning Fulfulde.

Like in many rural African settings (cf. Moore 2004), the motivation for learning different languages and the choice of which language to learn are influenced by local ideologies, driven by the need people have to belong and to successfully carry out their daily activities. There is no indication of a bias toward some idea of prestige in the language-learning process among the Mbororo. The generalization to be made is that Fulfulde clearly dominates, and apart from that, none of the languages has any greater prestige than the others. Reporting on a similar situation for the Mambila language cluster in the Adamawa Region of Cameroon, [START_REF] Connell | Language Diversity and Language Choice: A View from a Cameroon Market[END_REF] points to the fact that relationships among local languages in rural settings are not based on prestige. Instead, understanding multilingual behavior in such settings requires a knowledge of the details of the specific situation in which an interaction takes place. The assumption is that one language will be preferred over another depending on the respective domain of communication (Matras 2009, 45).

CONCLUSION

This study has examined a form of rural multilingualism among seminomadic cattle-rearers who live in the outskirts of Kejom Ketinguh, and showcases the pervasiveness of rural multilingualism. In total, twenty different languages are reported as being used by these pastoralist people, with four of the forty-seven consultants indicating that they were able to use more than ten languages each.

Mbororo children are monolingual in Fulfulde until the age of 5, after which other languages are learned for specific purposes. From this age, the need to socialize and communicate with non-Mbororo in Kejom Ketinguh motivates the Mbororo to learn CPE and Babanki. Subsequently, other languages are learned to facilitate their cattle-grazing activities, to assist them in carrying out commerce, and to help maintain social ties with people in other communities. The relationships among the languages in this setting are not based on prestige, with the motivation to learn different languages and the choice of which languages to learn being influenced instead by local ideologies.

We believe that this kind of study could be fruitfully extended to other Mbororo settlements across the North-West Region, not only to determine the number of languages used and which languages are learned but also to examine why the communities are multilingual.

NOTES

1. In this chapter, we will use "Kejom Ketinguh" to refer to the village, while "Babanki" will be used to refer to the indigenous people of the village and their language.

2. The Mbororo are known by different names: Cattle Fulani, Bush Fulani, pastoralist Fulani, Mbororo-Fulani, Felata, Fula, Fulbe, and so on. Approximately 80,000 of them live in the North-West Region of Cameroon (Amadou 2017, 38), and about 200 in Badem. They are predominantly Muslim.

3. Some participants reported that they have a good command of the languages they speak, while others did not, only being able to understand and exchange greetings. As it was impossible to assess the proficiency level of each consultant to determine what would count as multilingualism, we consider everyone who could actively or passively use more than two languages in communication to be multilingual.

4. English and French are the two official languages of Cameroon, inherited from the colonial experience. English is the language of education and administration in anglophone Cameroon (the North-West and South-West Regions), while French is used in the other eight regions of the country (francophone Cameroon).

5. Njamanjama is a green leafy vegetable grown in Kejom Ketinguh in large quantities and distributed to most major cities in Cameroon, particularly Bamenda, Yaoundé, and Douala.

Figure 1 . 1

 11 Figure 1.1 The Location of the Village of Kejom Ketinguh (the Lower Shaded Area on the Right) within Cameroon (Left). Source: Map created by the authors.

Table 1 .1 The Number of Participants by Sex, Age, and Highest Level of Education

 1

	Sex	Age Range Highest Formal Education	No. of Participants
	Female	1-5	None	2
		6-10	Primary	2
		11-40	None	3
			Primary	7
		41+	None	6
	Male	1-5	None	2
		6-10	Primary	2
		11-40	None	4
			Primary	12
		41+	None	6
			Primary	1

Source:


Pius W Akumbu

Babanki Verbal Extensions

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Introduction

The aim of this paper is to discuss the morphophonological processes that the addition of verbal extensions causes on Babanki verb roots 1 . Verbal extensions occur in Grassfields Bantu languages and their presence and identity have been established in a number of the languages including Kom [START_REF] Hyman | Proto-Bantoid verb extensions[END_REF], Bafut [START_REF] Mfonyam | Tone in the orthography of Bafut[END_REF][START_REF] Tamanji | A morphological study of verbal extensions in Bafut[END_REF][START_REF] Tamanji | A descriptive grammar of Bafut[END_REF], Mankon (Leroy 1982), Limbum [START_REF] Fransen | A grammar of Limbum: a Grassfields Bantu language spoken in Northwest Cameroon[END_REF], Isu [START_REF] Kiessling | Kausation, Wille und Wiederholung in der verbalen Derivation der westlichen Ring-Sprachen (Weh, Isu)[END_REF], Metaʔ [START_REF] Ngum | Verbal extensions in Meta[END_REF], and Babanki [START_REF] Akumbu | A pedagogic grammar of Babanki[END_REF]. [START_REF] Hyman | Proto-Bantoid verb extensions[END_REF] contains an extensive discussion of Babanki as well as a presentation and reconstruction of Proto-Bantoid verbal extensions. In Babanki, adding extensions to verb roots can cause several morphophonological changes on the verb, namely, vowel deletion, [f] strengthening and [s] weakening. While vowel deletion occurs after the glottal stop, root-final [f] strengthening, and [s] weakening occur when a CV extension is added. The extensions themselves are toneless and only receive tone from the verb root. This paper accounts for the changes using classical Generative Phonology and concludes that true word final consonants in Babanki are only nasals and the glottal 1 Babanki (Kejom, as the native speakers call their language and villages), is spoken in Babanki Tungo (Kejom Ketinguh) and Big Babanki (Kejom Keku) in the North West Region of Cameroon by approximately 39,000 people (Simons and Fennig 2018). As a Babanki native speaker I have provided the data used in this paper from my own speech, but also checked with four other native speakers, namely, Vivian Ba'ah (female, aged 35), Mbigeh Tigweh (male, aged 24) Vechese Dieudonne (Male, aged 23), and Tita Sherra (female, aged 21). I wish to sincerely thank all of them for making their knowledge on the language available and useful for the work done in this paper. stop, and that [f] and [s] are exceptional cases that verbal extensions seek to regulate. In the second section, I provide an overview of the phonology and morphology of Babanki, indicating the sounds that can occupy the final position of roots in the language, the verb roots and extensions they can take as well as the two-tone groups of the language. In §3, I discuss the effects that extensions can have on the verb roots and then provide a conclusion to the study in §4.

Overview of Babanki morphophonology

Phonology

As analyzed in [START_REF] Akumbu | Babanki coda consonant deletion and vowel raising: A case of allomorphy[END_REF], Babanki uses 25 phonemic consonants (Table 1)2 , 8 vowel phonemes (Table 2) and two level tones: H(igh) and L(ow). The segments combine into the CV, CGV, CVC and CGVC syllable structures, where G stands for glide.

Root-final Sounds

Vowels and consonants can occupy the final position of Babanki verb roots.

Of the eight phonemic vowels of the language, only /a/ does not occur in a CV root (1a). The six consonants that occur at the end of verb roots in the language are three nasals /m, n, ŋ/, two voiceless fricatives /f, s/, and the voiceless velar stop /k/ realized as [ʔ].

( The one-syllable roots can either have a CV or CVC structure whereas those with two syllables have a CV(C)CV structure. The first consonant can either be palatalized or labialized. It can also be seen in the data in (2) that the second of the two-syllable roots is always of the CV type, and that the V is always schwa. There are a good number of such roots that cannot stand alone without the second CV syllable also called 'formal extension'.

Extensions

The majority of what looks like two-syllable verbs results from the addition of a verbal suffix or extension3 to the root. At least five kinds of extensions are commonly found on verb roots, as illustrated below (cf. Hyman 2013 for additional discussion):

The extensions appear in (3) with the same tones as the preceding verb roots and the most straightforward analysis is that extensions are toneless and only receive tone from the verb root and the inflectional morphology. Thus, in the progressive aspect, the extensions bear the progressive low tone while in the imperative mood, they bear the imperative high tone (see §4.4 for the imperative).

Lexical tones

As seen in the following minimal pairs, verb roots fall into two tone classes, L and H [START_REF] Akumbu | Babanki verb tone[END_REF].

L tone verbs H tone verbs

(4) fuʔ 'bubble' fuʔ 'tune' də m 'grunt' də ḿ 'play' fas 'break' faś 'threaten' zhwì 'pant' zhwí 'kill' mò 'narrate' mó 'deny' shisə ̀ 'remove' bośə ́ 'melt' myə tə ̀ 'complete' b�ńsə ́ 'lure to sleep'
As already mentioned, if the verb is bisyllabic, both syllables will be LL or HH.

Extensions and Verb Phonology

Adding a CV extension to a verb root can cause several morphophonological changes on the verb, namely vowel deletion after the glottal stop (CVʔV→ CVʔ), strengthening of /f/ (CVf→CVb) and weakening of /s/ (CVs→CVy).

Vowel Deletion

As stated earlier, there are two-syllable stems in the language whose second syllable begins with a glottal stop, followed by a vowel identical to that of the first syllable. When extensions are added to such roots, the vowel of the second syllable is deleted consistently:4

( One may argue that the glottal stop is not allowed verb finally and that it requires the echo-vowel, that is, that the vowel is inserted after a glottal stop if it is final. However, there are numerous instances where the glottal stop occurs in final position but does not require the insertion of an echo-vowel:5

The data in (6) show that the glottal stop is capable of occupying final position and that the process in ( 5) is actually that of deletion of the echovowel when extensions are added. The forms in (7a) have a nasal coda and a schwa is inserted in the imperative to bear the high imperative tone (see §4.4). In (7b) where the roots end in the glottal stop, the root vowel spreads to the final position to bear the imperative tone. However, in (7c) which contains the echo-vowel (underlyingly), that vowel bears the imperative tone, confirming that the echo-vowel is actually deleted when an extension is attached. The deletion process in (5) can therefore be captured by the following rule:

(8) Vowel Deletion V → Ø/VC___+CV
According to the rule, a vowel is deleted when preceded by a VC and followed by a CV at a morpheme boundary as illustrated in the following derivation.

(9) UR/maʔa-lə byiʔi-tə shiʔi/ Tone assignment maʔa

-lə ̀ byiʔi-tə ́ ___ Vowel Deletion maʔ-lə ̀ byiʔ-tə ́ ___ PR[ maʔlə ̀ byiʔtə ́ shiʔi]

[f] Strengthening

When The data in ( 15) indicate that the process occurs only within stems, specifically due to the addition of an extension. The data in (21b) show that the only context where [y] alone can occur is when the following consonant is [m] (*taḿmə , etc.). Elsewhere, [s] is capable of assimilating the features of the following consonants resulting to consonant gemination. Therefore, [s] assimilates to a lingual consonant, not a labial one.

[s] Weakening

Imperative Tone and Extensions

The imperative is marked in Babanki by a floating high tone. When the root of one-syllable verbs has a low tone, a schwa is inserted (i.e. suffixed) as in (22a) to bear the imperative tone [START_REF] Akumbu | Babanki verb tone[END_REF]. This might happen in order to avoid a rise on a single vowel because contour tones are rare in Babanki:

(

Conclusion

The discussion in this paper has centered around the morphonological processes that the addition of verbal extensions cause on Babanki verb roots. It has been demonstrated that adding extensions to verb roots can lead to either post-glottal vowel deletion, [f] strengthening, or [s] weakening. [f] strengthening and [s] weakening occur in similar contexts and in each case a fricative is realized as a more or less homorganic stop or approximant. There is therefore a constraint in Babanki that prohibits the occurrence of fricatives before consonants in a cluster. It has been shown that the process occurs only within stems, specifically due to the addition of an extension. It remains unclear, though, why the change from [s] rather goes to the approximant whereas the alveolar stop is available in the language. This irregularity explains, in part, the tendency by some speakers to move towards consonant gemination when [s] assimilates to lingual consonants. In addition, it has been explained in this paper that the extensions are toneless and only receive tone by rightward spread from the verb root.

Table 1 : Consonant Phonemes

 1

		Bilabial Labiodental Alveolar Postalveolar Palatal Velar
	Stops	b	t, d		k , g
	Nasals	m	n	ny	ŋ
	Fricatives	f, v	s, z	sh, zh	gh
	Affricates	pf, bv	ts, dz	ch, j
	Liquids		l
	Approximants	w		y
	Table 2: Vowel Phonemes
		Front	Central	Back
	Close	i	ɨ	ʉ	u
	Close-Mid	e		o
	Open-Mid		ə
	Open		a

One-syllable Two-syllable (with formal extensions)

	1)	a.	shí	'take'
			nú	'defecate'
			f� ̀	'exit'
			chʉ ̀	'soak'
			shə ́	'slice'
			chò	'pass'
		b.	z� ḿ	'wither'
			teń	'push'
			kaŋ	'fry'
			ch� f	'advise'
			bis	'scatter'
			kúʔ	'rise'
	3. The Verb
	3.1 Verb Roots
	Only one-syllable roots are attested in Babanki except when there is verbal
	reduplication (Akumbu & Chibaka 2012, Akumbu 2015). The verb roots that
	appear to have two syllables always have a CV ending, which can be
	interpreted as an extension. Nevertheless, there are formal extensions that
	occur with roots that otherwise do not occur alone. Examples of the one-
	syllable roots and the lexicalized CV(C)-CV are given below.
	(2) saŋ	'dry'	gitə ̀	'add'
	chò	'pass'	baŋlə ̀ 'dodge'
	vì		'come'	shisə ̀ 'remove'
	buḿ 'hunt'	toŋtə ́ 'sift'
	fə ŋ	'fall'	faʔtə ́ 'hurry up'
	kweń 'enter'	b� ʔsə ́	'ignore'

  'reduce' fafə ̀ 'reducing' kə ŋfaf 'reduction' ə ́↓chof 'to shout' chof 'quarrel' chofə ́ 'quarreling' kə ǹchof 'quarreling'The occurrence of [f] is widespread and that of [b] is limited to the context where a consonant cluster results from the addition of an extension. It is seen that [f] occurs initially, intervocalically, finally, but not preconsonantally. The same is found with formal extensions where [b] is required instead of [f]: It happens that [f] strengthening does not apply across words. If the C is in the next word, then the fricative survives:

		by� f	'get bad'	by� b-sə ́	'destroy'
		laf	'dress up'	lab-sə ́	'dress someone up'
	(15)	ts� f l� f ə ǵuf wiʔ' zaf ə ḱaf wuńdoŋ 'beckon a friend' 'push' ts� b-lə ́ 'hurry' 'to pull someone' l� b-lə ́ 'ache' zab-kə ́	'push someone around' 'hurry' 'feel pain'
		chof guf ə by� f nańtô 'shout' 'pull' 'become too bad' chob-kə ́ 'pick a quarrel' gub-mə ̀ 'argue'
		kwof	'snatch'	kwob-mə ́ 'snatch several times or by
					several people'
	The data show that the change in the root consonant is caused by the
	addition of the extensions. It can be argued, though, that the change is rather
	from [b] to [f] in final position. However, several other contexts show the
	occurrence of the fricative providing evidence that /b/ occurs at the end of a
	syllable when an extension is added:
	(11) Infinitive		Imperative.	Progressive	Derived Noun
	ə faf 'to reduce' fafə ́ (12) lobtə ́ 'deceive'
		tabtə ́	'solidify'
		tabkə ̀	'struggle'
		nyablə ̀	'maltreat'
	The change from [f] to [b] can be captured by the following rule.
	(13)	[f] strengthening
		/f/ → [b] /__+C
	The rule states that the voiceless labiodental fricative becomes the voiced
	bilabial plosive when followed by a consonant at morpheme boundary. The
	data in (10) are therefore derived as follows:
	(14) Tone assignment extensions are added to verb roots that end in [f], the voiceless UR/ laf-sə guf-mə l� f/ laf-sə ́ guf-mə ̀ __ labiodental fricative changes to [b]: f strengthening lab-sə ́ gub-mə ̀ __
	(10)	kaf	'beckon' PR [ labsə ́ kab-tə ̀ gubmə ̀ 'beckon several times' l� f]
		faf	'reduce'	fab-tə ̀	'reduce a bit'

  It should be mentioned that the tendency is for [s] to assimilate the features of the following extension consonant and result to consonant gemination. Consider the alternative way of producing the forms in (16a) shown in (21a).

	According to the rule, the voiceless alveolar fricative becomes the palatal
	glide when followed by a consonant at morpheme boundary. If C occurs in
	the next word then [s] Weakening does not apply:
	(19)	ə bas kə mbò	'to tear a bag'
		ə ḱaś tà ə kə ʔ	'to twist only the face'
		ə fwos nańtô 'fart too much'
	This means that the process takes place only within a stem that results from
	the addition of an extension as illustrated in the following derivation.
	If the verb root final consonant is [s], it changes to [y] when an extension is (20) UR / taś-mə bis-tə sas-kə taś-sə/
	added to the verb: Tone assignment	taś-mə ́	bis-tə ̀	sas-kə ̀	taś-sə ́
	s deletion or fusion	__		__	__	ta-sə ́
	(16) a. kaś s weakening	'twist (face)' kaýtə ́ 'twist (face) again and again' taý-mə ́ biỳ-tə ̀ saỳ-kə ̀ __
		bis	'scatter' PR[ taýmə ́ biỳtə ̀ biỳtə ̀ 'scatter several times' saỳkə ̀	ta-sə ]
		bas	'cut open'	baỳlə ̀	'cut open in several places'
		zas	'loosen'		zaỳlə ̀	'loosen several times'
		sas	'scatter'	saỳkə ̀ 'scatter into several pieces'
		fwos 'fart'		fwoỳkə ̀ 'fart repeatedly'
		b. taś	'surround'	taśə ́	'surround'
	kaś (21)a. kaś	'twist (face)' kaśə ́ 'twist (face)' kattə ́ 'twist one's face again and again' 'twist (face) again and again'
		bis bis	'scatter' 'scatter'	bisə ̀ bittə ̀	'collapse' 'scatter several times'
		bas bas	'break' 'cut open'	basə ̀ ballə ̀ 'break up' 'cut open in several places'
		zas	'loosen'	zallə ̀	'loosen several times'
	The data in (16a) illustrate that when extensions that begin with [m, t, l, k] are sas 'scatter' sakkə ̀ 'scatter into several pieces'
	combined with roots that end in [s], it changes to [y]. The forms in (16b) fwos 'fart' fwokkə ̀ 'fart repeatedly'
	show that if the [-sə] extension is added to such roots, [s] weakening does not b. taś 'surround' taýmə ́ 'mix up'
	apply but one of the alveolar fricatives is deleted, that is, deletion by identity bis 'scatter' biỳmə ̀ 'collapse'
	takes place: ss→ s. It must be the case that the deletion precedes [s] bas 'break' baỳmə ̀ 'break up'
	weakening. Again, it can be argued that the change is rather from [y] to [s] in
	final position but this is dismissed by the fact that [y] occurs only before a
	consonant whereas [s] occurs in several other contexts:
	(17) Infinitive	Imperative	Progressive	Derived Noun
	ə bis' to scatter' bisə ́ 'scatter'	bisə ̀ 'scattering'	kə mbis 'scattering'
	ə ḱaś 'to twist' kaś 'twist'	kaśə ́ 'twisting'	kə ŋkaś 'twisting'
	The rule in (19) captures the change from [s] to [y].
	(18)	[s] Weakening
		/s/ → [y] /__+C

  It has been noted earlier that extensions are toneless in the language and receive a tone by spreading from the verb root as soon as they are attached. If, however, the construction is in the imperative mood, the floating high imperative tone is introduced as shown in the following derivation.

			guf	'pull!'		gufə ́	'argue!'
		b.	by� f	'get bad!'	by� f	'destroy!'
			laf	'dress up!'	laf	'dress someone up!'
			fwoś 'stir!'		fwoś	'stir continually!'
	When extensions are added to imperative constructions, they consistently
	take a high tone irrespective of whether the verb root is L (23a) or H (23b).
	(23)	a.	kaf	'beckon!'	kab-tə ́ 'beckon several times!'
			faf	'reduce!'	fab-tə ́ 'reduce a bit!'
			sas	'scatter!'	saỳ-kə ́ 'scatter into several pieces!'
			fwos 'fart!'		fwoỳ-kə ́ 'fart repeatedly!'
			bis	'scatter!'	biỳ-mə ́ 'collapse!'
		b.	by� f	'get bad!'	by� b-sə ́ 'destroy!'
			laf	'dress up!'	lab-sə ́ 'dress someone up!'
			ts� f	'push!'		ts� b-lə ́ 'push someone around!'
			l� f	'hurry!'		l� b-lə ́	'hurry!'
			taś	'surround!'	taý-mə ́ 'mix up!'
	(24)			UR /kaf-tə		fwos-kə	taś-mə/
	Imperative tone assignment	kaf-tə ́	fwos-kə ́	taś-mə ́
	f strengthening			kab-tə ́	__	__
	s weakening			__		fwoỳ-kə ́ taý-mə ́
				PR [ kabtə ́	fwoỳkə ́	taýmə ]
	22)	a.	bas	'cut!'		basə ́	'cut up!'

The IPA counterparts for the following orthographic symbols used in this paper are given in square brackets: ny[ɲ], sh[ʃ], zh[ʒ], gh[ɣ], ch[tʃ], j[dʒ], y[j].

Verbal extensions in Babanki fall short of what is typical of Narrow Bantu in that some of the extensions in the latter have no correspondences in Babanki, e.g. 'applicative', 'passive', 'middle' (impositive). Most of these functions, where present at all, are based on combinations of autonomous lexical items. The common extensions are morphemes for 'attenuative', 'intensity', and 'repetitive', with different forms for the latter based on whether the verb is transitive or not. (3) -sə -kə -tə -lə -mə vi-sə ̀ 'bring near' bvɨkə ̀ 'fail repeatedly' myə -tə ̀ 'complete' ko-lə ̀ 'scrape many times' kwoʔmə ̀ 'think together' kum-sə ̀ 'touch' taǹ-kə ̀ 'fly' baʔ-tə 'scrape' daŋ-lə ̀ 'spread' su-mə ̀ 'insist continually' shisə ̀ 'remove' cho-kə ̀ 'pass repeatedly' bum-tə ̀ 'meet someone' si-lə ̀ 'caress many times' cho-mə ̀ 'pass many times' kweń-sə ́ 'send inside' fə ŋ-kə ́ 'fall repeatedly' baʔ-tə ́ 'arrange' kaŋ-lə ́ 'fry in part' pfwo-mə ́ 'return' beń-sə ́ 'make dance' kaʔ-kə ́ 'turn around' te-tə ́ 'select' te-lə ́ 'insult many times' faŋ-mə ́ 'gather lots of things' bwoḿ-sə ́ 'praise' bwi-kə ́ 'give birth a lot' ny� ŋ-tə ́ 'run hurriedly' faʔ-lə ́ 'pin many times' so-mə ́ 'melt'

In a Babanki File maker Pro™ database of 2,005 lexical entries[START_REF] Akumbu | Kejom (Babanki)-English lexicon. Bamenda: Ga'a Kejom Development Committee[END_REF]), 14 verbs have been found with an echo-vowel after the glottal stop.

There are 86 CVʔ roots in the database of 2,005 lexical entries.


Paolo Maistri
email: paolo.maistri@univ-grenoble-alpes.fr

Jiayun Po

A Low-Cost Methodology for EM Fault Emulation on FPGA

Keywords: EM fault injection, emulation, clock glitching, FPGA, RTL

In embedded systems, the presence of a security layer is now a well-established requirement. In order to guarantee the suitable level of performance and resistance against attacks, dedicated hardware implementations are often proposed to accelerate cryptographic computations in a controllable environment. On the other hand, these same implementations may be vulnerable to physical attacks, such as side channel analysis or fault injections. In this scenario, the designer must hence be able to assess the robustness of the implementation (and of the adopted countermeasures) as soon as possible in the design flow against several different threats. In this paper, we propose a methodology to characterize the robustness of a generic hardware design described at RTL against EM fault injections. Thanks to our framework, we are able to emulate the EM faults on FPGA platforms, without the need of expensive equipment or lengthy experimental campaigns. We present a tool supporting our methodology and the first validations tests done on several AES designs confirming the feasibility of the proposed approach.

I. INTRODUCTION

Many applications nowadays require confidentiality, integrity, and authentication, which can be achieved through the implementation of cryptographic primitives. It is hence quite common to find these implementations in many embedded systems, either as software or, if demanded by requirements in terms of performance or efficiency, as hardware designs.

Although cryptographic algorithms can be considered reasonably secure, it is however well known that careless implementations of the secure primitives can nonetheless reveal critical information. This kind of attacks directed to the actual implementation can be passive [1] [START_REF] Kocher | Differential Power Analysis[END_REF], where the behavior of the system is observed and analyzed, or active [START_REF] Bar-El | The Sorcerer's Apprentice Guide to Fault Attacks[END_REF], where the regular functioning is altered in order to gather useful information about the data being processed.

The correct behavior of the device can be altered in several ways, with the usual goal of injecting some computational error that will be further analyzed and exploited in order to break the cryptosystem. Fault injection attacks can be performed by using a variety of techniques: voltage and clock glitches, laser or EM illumination, etc. All these techniques have different properties in terms of precision, required knowledge, and cost. Glitches, for instance, are quite simple and cheap to implement but act on global signals of the integrated circuit (e.g., the clock or the voltage supply), so they affect the design in its entirety: for this reason, they are mostly effective against software implementations (running on CPUs or microcontrollers), where the serial execution of the code limits the error propagation. On the other hand, their impact on hardware implementations is much less predictable or controllable: hence, secure hardware implementations are usually attacked through laser or, more recently, EM fault injections (EMFI), which exhibit good spatial locality and excellent temporal precision. In particular, laser fault injection (LFI) has excellent controllability even when attacking reasonably recent technology nodes [START_REF] Dutertre | Sensitivity to Laser Fault Injection: CMOS FD-SOI vs. CMOS Bulk[END_REF]: on the other hand, the cost in terms of equipment, preparation, and related expertise is not affordable for everybody. EMFI attacks, while still providing good potential from the point of view of the attacker, are more accessible and are thus becoming an interesting attack technique in the recent literature.

For these reasons, designers must hence take into consideration such threats as early as possible, in order to assess the vulnerability of the architecture against physical attacks and propose solutions (i.e., countermeasures) at all levels in order to face these threats. This may constitute a serious challenge: protecting as early as possible means that solutions must be proposed at software (if it is the case) or Register Transfer Level (RTL), when there may be no actual silicon yet to perform the experiments.

In this work, we want to propose a methodology aimed at validating the architectural consequences of EM fault injections. Our framework does not aim at being an alternative attack technique nor a generic fault injection framework, but it allows emulating the EM fault on a configurable platform (an FPGA board) by mimicking the spatial and temporal characteristics of EM pulses on any digital designs, without any additional equipment other than a programmable board. Thanks to our approach, designers can therefore validate architectural solutions with respect to a fast, inexpensive, and accurate flow. We have validated the methodology on three different hardware implementations of the Advanced Encryption Standard, proving that exploitable faults, issued from literature models, can be easily injected. This paper is organized as follows. In the next section, we resume the existing state of the art, which constitute also the motivation behind this work: we briefly describe the experimental platforms for EMFI, and the main abstractions that have been proposed to model the interaction between the EM pulse and the silicon. Section III describes our methodology more in detail, highlighting the different steps of our approach. First preliminary results are elaborated in Section IV, along with some perspectives on future research directions. Finally, Section V concludes the paper. *Institute of Engineering Univ. Grenoble Alpes II. MOTIVATION Electromagnetic Fault Injection (EMFI) has been gaining in popularity in the recent years. EMFI does not require special preparation of the integrated circuit (i.e., no backside access for illumination, no lapping in order to expose the silicon layers) and the experimental setup is of lower complexity: a pulse generator, an injection probe, and a control machine are the main components of the platform (with the target as well). After a first period when experimental platforms were mostly built using commercial or home-made parts, a few complete platforms have recently made their appearance on the market [START_REF] Toulemont | A Simple Protocol to Compare EMFI Platforms[END_REF]. Nonetheless, these setups still constitute an important investment [START_REF]ChipShouter User Manual[END_REF]. Some studies have explored alternative solution to improve the interaction between the probe and the circuit, but are mostly oriented to passive analysis [START_REF] Toulemont | Exploring flexible and 3D printing technologies for the design of high spatial resolution EM probes[END_REF].

For these reasons, it is important to understand the mechanisms of error injections due to EMFI. Several studies have appeared in the latest years, aiming at modelling at different levels the effects in both hardware and software implementation of cryptographic algorithms. In [START_REF] Dehbaoui | Electromagnetic Transient Faults Injection on a Hardware and a Software Implementations of AES[END_REF], AES was attacked by EMFI both in software, running on an 8-bit microcontroller, and on a hardware iterative design implemented on FPGA. Although the fault model of the two campaigns was not directly comparable, the authors were nonetheless able to propose and validate some initial guess about the error injection mechanism: according to their conclusion, the most likely fault model was due to localized timing violations. The authors did not prove the assumption from a formal point of view, but their experimental validation of a timing countermeasure seemed to confirm their assumptions. This similarity was also confirmed in later works, such as [START_REF] Moro | Formal verification of a software countermeasure against instruction skip attacks[END_REF].

Nonetheless, the understanding of the actual mechanisms occurring during EMFI is not as simple as that. Several other studies have shown that timing faults are only part of the global picture, as the EM pulse can disrupt the set/reset mechanism of flip-flops in a subtler way [START_REF] Ordas | Electromagnetic fault injection: the curse of flip-flops[END_REF]. This mechanism has been later detailed as a double interaction with the power grid [START_REF] Dumont | Modeling and Simulating Electromagnetic Fault Injection[END_REF], as the EMFI creates two opposite pulses within the circuit. While the first lowers temporarily the supply voltage (thus creating timing violations), the second restores it and possibly interferes with the DFF sampling. This is confirmed by the fact that the experiments heavily depend not only on physical location of the injection, but on its exact timing as well [START_REF] Menu | Experimental Analysis of the Electromagnetic Instruction Skip Fault Model[END_REF].

Despite the complexity of the actual interaction between the EM pulse and the gates, it is generally accepted that EM faults can be approximated by timing faults in a first instance [START_REF] Ghodrati | Inducing Local Timing Fault Through EM Injection[END_REF]. This assumption was thus adopted in [START_REF] Surya | Local Clock Glitching Fault Injection with Application to the ASCON Cipher[END_REF], where the authors have shown the feasibility of using internal primitives of an FPGA to create clock glitch at a local level. However, their approach was limited to just evaluate the impact of the modification on resource usage and on performance, without any actual analysis of the faults that could be injected. Additionally, their methodology was applied manually on a specific design (namely, a lightweight ASCON architecture) and in a specific location.

In this paper, we want to show that an automated approach can be generalized on any design and that exploitable faults can be injected. We describe our methodology in the next section.

III. METHODOLOGY

A. Basic Principles

Our goal is to control timing violation faults in any part of the design. This fault model is quite specific to EM fault injection, as highlighted in the previous section: other fault attacks (or general reliability assessments) may be based on different fault models, such as bit-flip or bit set/reset. In order to accomplish this result, we instrument the design in order to create a clock glitch only in the specific part that has been defined as the target of the injection: as a consequence, we can emulate the sampling faults that would occur in the gates when targeted by EM injections. This approach first requires a clock glitch to be generated internally in the design and routed to the target. The second constraint is time-related: the glitch must occur only when needed, and nominal conditions (i.e., the regular clock) should be in general restored immediately after the glitch. The triggering condition can be set by the designer, but it is usually based on a custom delay with respect to a specific event (e.g., the start of the encryption).

Although these two conditions seem easy to satisfy, there are some details that require attention from the designer. First, the spatial granularity of the fault injection: in principle, the target can be from a single flip-flop up to an entire module. In practice, if we aim at emulating local faults, smaller granularities should be used (such as a few FFDs or a specific register), as our goal is not to emulate global clock glitches. More advanced methods can be envisioned, as suggested in Section IV. Secondly, the glitch may occur either on the rising or the falling edge of the clock signal, or even both: different policies may cause different behaviors, depending on the actual design under attack, and should be taken all into consideration. In order to minimize the modifications to the original design, all the additional blocks (glitch generator, trigger, etc) can be defined separately in a larger wrapper module, containing the target as well, as schematically shown in Fig. 1.

The glitch can be generated and controlled by using two synchronous clocks in the designs: the regular and the faultable clocks. The latter clock will be used to drive only the cells within the target (i.e., the flip-flops where the fault has to be injected), while the former will be used by the rest of the design. The two clock signals can be created through the FPGA Digital Clock Manager (DCM), and managed by the Fault Injector module. When the trigger is off no glitch is injected, meaning that the two clocks are identical; during the injection, the faultable clock (and only this clock) is perturbated with the glitch, and the sampling in the corresponding targets is corrupted. After the glitch, the two clocks are again identical, which allows resuming the computation process without any further error. The faulty output can then be recovered for cryptanalysis.

B. Tools and Implementation

Our proposed methodology is largely based on existing FPGA design flows. This is justified by the fact that our goal is to emulate EM injections to evaluate architectures and countermeasures at RTL or higher level: FPGA platforms are therefore perfectly suited, thanks to their configurability and large spectrum of devices. We have used Xilinx devices, but any other programmable board can be used if the main requirements are met.

In order to generate the glitch internally, we rely on the BUFGCTRL primitive available on Xilinx FPGAs [START_REF]7 Series FPGAs Clocking Resources[END_REF]. These components are well known clocking resources that can be used to switch between two input clocks without any glitch when properly configured. It is important to highlight that in our case, the glitch-free property of the primitive ensures that we can finely control the clock output: if a glitch occurs, it is deterministically due to our trigger and not to undefined behavior of the logic itself. This behavior can be achieved by configuring the additional inputs, namely the Ignore, Enable, and Selection input pins, to specific values.

The clock switching is controlled by a decrementing counter, When the counter reaches the activation value, BUFGCTRL is triggered and changes to the secondary input clock. In order to preserve the global synchronization of the computation process, the regular clock is then restored. To simplify this step, the clock switch occurs when the counter reaches 1, and restores the normal clock at 0. The generic setup for glitch generation is shown in Fig. 2. The main clock is the nominal clock of the system; the auxiliary clock is used for glitch generation, and it is selected by the BUFGCTRL primitive when the trigger is activated. Its actual shape can be chosen to create a glitch with a specific pattern: in our experiments we set it to the same frequency of the main clock, a duty cycle of 25%, and a phase shift that depends on the design under test (270° in our case), but the actual configuration may be tailored to the specific experiment. The trigger is updated on the main clock, but its edge sensitivity depends on the type of glitch (rising, falling, or both edges) that has to be injected.

A tool has been implemented in Python to automate the instrumentation process. It has been designed to accept any netlist in Verilog, which allows to easily process any synthesizable design. The tool identifies all possible targets by scanning the netlist and looking for keywords defining the sequential logic. Hierarchical or flattened designs are equally supported, while the list of keywords can be configured to adapt to different technology targets. The user is then allowed to choose a subset of targets, or the tool can be instructed to go through the list element by element for an extensive emulation campaign. The auxiliary clock, the triggering blocks, and the proper clock connections are handled directly by the tool in a transparent way for the user. The instrumented design can thus be used to replace the original one on the programmable board for the accelerated emulation experiment. In the perspective of comparing the results from this methodology against actual EMFI, the tool can optionally define a separate partition for the target in an automatic way, while the rest of the design is placed far from the target. This will allow easier placement of the EM probe during the attacks and the results will be more representative of the actual sensitivity of the selected target (and not of other glue logic).

C. Validation

The methodology was validated on three different hardware implementations of the Advanced Encryption Standard [START_REF]Advanced Encryption Standard[END_REF]: a trivial iterative design, an architecture protected by an Error Detecting Code (EDC) [START_REF] Bertoni | Error analysis and detection procedures for a hardware implementation of the advanced encryption standard[END_REF], and a design protected by hybrid temporal redundancy [START_REF] Maistri | Double-Data-Rate Computation as a Countermeasure against Fault Analysis[END_REF]. At this stage, no extensive campaign was performed to evaluate the countermeasures, as the main goal was rather to confirm the feasibility of the approach on designs having disparate constraints. All the designs were implemented on a Nexys A7-100T board, which is equipped with a Xilinx Artix-7 programmable chip. This board was chosen because of its large availability of clocking resources, and because the FPGA circuit is not protected by any heat spreader, making thus easier to plan later EM fault injection campaigns.

Several experiments were done in order to find the most suitable value for configuring the parameters of the glitch generation, in particular the frequency, phase, and duty cycle of the auxiliary clock, as well as different techniques to create effective glitches. More importantly, several tests were run on all designs to inject errors on different elements of the designs (e.g., all the state bytes) and at different times (i.e., different encryption cycles). Our experiments have shown that faults at byte level can be successfully injected anywhere and anytime in the design, by controlling the clock glitches at local level. As an example, we report the output of an encryption experiment in Fig. 3, where a standard pair of plain text and key from the NIST specifications were used for correct and a faulty encryption on the EDC-protected design. In this experiment, a clock glitch was injected on the output of the SubBytes operation on the least significant byte of the state during the 8 th round. The figure highlights how the output of the faulty encryption is fully corrupted as expected, and the cryptanalysis by reverse computation of the result correctly identifies the error as occurring on the targeted byte and round, thus confirming the successful injection. Moreover, the injected error value can be guessed as well.

IV. DISCUSSION

This methodology has been proposed to emulate EM fault injection on an FPGA without recurring to an actual experimental EM platform. The designer can then apply classical fault analysis on the experimental results in order to assess the exploitability of the faults.

The short-term objectives are comparing the results with actual EM injected faults, and evaluate architectural countermeasures against fault attacks. Although only dedicated designs were presented in this work, the methodology can be easily applied to any synthesizable description of any architecture: for instance, it may be used to analyze the error propagation within the architecture of a general-purpose processor. The main requirement is that the netlist description has to be available and modifiable to allow clock instrumentation, such as in RISC-V architectures. If the netlist is encrypted, our approach cannot be used.

The parameter exploration is currently delegated to the designer, who needs to tune the fault injector module in order to fit the target constraints and find the best configuration. This may be a tedious process, which could be sped up with proper assistance from the tool if the longest path delay would be known for the given target. Functional relationship analysis might be exploited as well in order to identify sets of targets and estimate spatial locality at RTL as in [START_REF] Papadimitriou | A multiple fault injection methodology based on cone partitioning towards RTL modeling of laser attacks[END_REF]. This methodology, originally proposed to create a laser-based fault model at RTL, could be effectively applied also to EM faults as well, thanks to similar spatial properties of the two attack techniques.

So far, only single glitches have been taken into consideration. On the other hand, current FPGAs have several clocking resources available on chip, which would allow for multiple glitch domains at the same time. The device used in our experiments, for instance, has 6 clock management tiles, which can be used to create independent glitches in parallel. Triggering conditions may be further explored as well. In simple attacks, only one glitch is injected at a specific time, but a more advanced controller could be programmed to schedule more than one glitch for each execution. When combined with independent parallel glitching, cited above, this would allow emulating complex higher-order attacks, with spatial and temporal multiplicity higher than one.

V. CONCLUSION

Physical attacks are a well-known threat to embedded secure systems, and electromagnetic injections are an effective way to carry out fault attacks. Designers must therefore assess the vulnerability of implementations as early as possible in the design flow. In this paper, we present a methodology that can emulate EM faults by exploiting local timing violations. The proposed approach can help the designer to validate architectural countermeasures at Register Transfer Level against a realistic fault model on an actual prototype implemented on FPGA, without the need of an expensive EMFI platform.

The methodology has been fully implemented and the developed tool is being published and made accessible to the community. Exploitable faults have been injected into several designs. In the short term, the injected faults will be compared to those obtained by an actual EMFI platform, and error detecting countermeasures will be evaluated with the proposed approach.

Fig. 1 .

 1 Fig. 1. Clock signals in the design, and how they are generated. Red color shows new or modified elements of the design.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Clock signals in the design, and how they are generated

ACKNOWLEDGMENT

This work has been partially supported by the French National Research Agency in the framework of the "Investissements d'avenir" program (ANR-15-IDEX-02).


Pius W Akumbu

Noun class 9/10 tone in Central Ring Grassfields Bantu: An overview

Singular and plural noun roots in Grassfields Bantu languages may have different phonological

Introduction

It is possible to have different tones on singular and plural forms of nouns in Grassfields Bantu languages. While this is not unique to this group of languages, the variation here proves to be complex and difficult to describe. Central Ring Grassfields languages (CRGL) of Northwest Cameroon are subject to a variety of complex tonal changes and present an intricate relationship particularly between the tones of the singular nouns (class 9) on the one hand and those of the plural (class 10) on the other. Previous descriptions have raised the issue and discussed the complexity in some of the languages (e.g. Babanki (Hyman 1979a, 1980a, 1980b[START_REF] Akumbu | Nasals and low tone in Grassfields noun class prefixes[END_REF], and Oku (Davis 1992, 1997, Hyman 2014)), yet it remains unclear why and how the tonal differences manifest in the rest of the CRGL. I attempt a unified analysis of the tonal intricacies within Autosegmental Phonology. Some of the data presented come from existing literature while the rest have been collected directly from native speakers. The study provides support for the claim that floating tones are central to the analysis of Grassfields Bantu languages [START_REF] Hyman | Floating tones in Mbam-Nkam[END_REF]. The languages under study are presented in §2 followed by the review of related literature in §3. Class 9/10 tone is discussed in §4 and a brief conclusion is given in §5.

Central Ring Grassfields languages

The CRGL on which the present study focuses are a sub-group of Grassfields Bantu (a branch of Benue-Congo and a sister of the Narrow Bantu languages). Although closely related to Narrow Bantu, Grassfields Bantu languages show remarkable differences in nearly all parts of their grammar. The CRGL themselves have many features in common and a comparison of shared vocabularies between immediate neighbors, such as Babanki and Kom [START_REF] Brye | Rapid appraisal sociolinguistic research among the Babanki ALCAM 824[END_REF] show that they share at least 70% of their vocabulary. Until recently, only five languages (Kom, Oku, Babanki, Mmen and Bum) have been listed as Central Ring languages [START_REF] Dieu | Atlas linguistique du Cameroun (ALCAM): Inventaire préliminaire[END_REF][START_REF] Breton | Atlas administratif des langues nationales du Cameroun[END_REF][START_REF] Watters | Grassfields Bantu[END_REF]). However, it has now been proposed that Kuk and Kung also belong to this subgroup [START_REF] Tatang | Aspects of Kung grammar[END_REF], Simons & Fennig 2017). There are nearly 400,000 people who speak the languages, as follows: Kom 233,000, Oku 40,000, Babanki 39,000, Mmen 35,000, Bum 21,000, Kuk 3,000, and Kung 1,750 (Simons & Fennig 2017).

Previous studies on noun classification in Central Ring

A lot is known about Grassfields Bantu languages in general and the noun classes in particular (Hyman & Voorhoeve 1980, Hyman 1980b, 1980c[START_REF] Stallcup | La géographie linguistique des grassfields[END_REF][START_REF] Williamson | The noun prefixes of New Benue-Congo[END_REF][START_REF] Watters | Southern Bantoid[END_REF][START_REF] Watters | Grassfields Bantu[END_REF][START_REF] Piron | Identification lexicostatistique des groupes bantoïdes stables[END_REF], Kießling 2010, etc.). Studies on Central Ring languages have also identified and described different aspects of the noun class systems.

As shown in Table 1, CRGL can have 11, 12 or 13 noun classes marked by either prefixes and/or suffixes. Hyman (1980b), [START_REF] Yuh | The noun class system of Kom[END_REF], [START_REF] Jones | Tone in the Kom noun phrase (Part 2)[END_REF][START_REF] Shultz | Kom Language Grammar Sketch Part 1[END_REF] have identified 13 noun classes in Kom with class 9 marked by ø, or N-, and class 10 by the -sé suffix. Mmen also has 13 noun classes with ø, or Nfor class 9 and the seprefix for class 10 [START_REF] Chiatoh | The noun class system of Mmen[END_REF][START_REF] Kießling | Infix genesis and incipient initial consonant mutations in some lesser known Benue-Congo languages[END_REF][START_REF] Möller | The noun and verb in Mmen, a center Ring Grassfields Bantu Language[END_REF][START_REF] Möller | Nominal tone in Mmen, A Grassfields Bantu language of Cameroon[END_REF]. The other language in this subgroup with 13 noun classes is Oku as seen in Hyman (1980b), Davis (1992, 1997[START_REF] Mbibeh | The noun class system of Oku[END_REF]. Class 9 is also marked by ø, or Nwhile class 10 takes the -sə́ suffix. Babanki on its part has 12 noun classes with ø, or Nprefix for class 9 and -sə́ for class 10 (Hyman 1979a, 1980b, Akumbu 2011[START_REF] Akumbu | A pedagogical grammar of Babanki[END_REF]. Hyman (1980b) and Akumbu (2009) reveal that Bum also has 12 noun classes. Class 9 in this language can be marked by one of the following: ø, N-, àwhile class 10 can take either a prefix or a suffix: sə-, sú. Kießling (in preparation) shows that Kuk has 12 noun classes with class 9 marked by ø, or Nwhile class 10 takes a səprefix. Finally, Kung has been shown to have only 11 noun classes with class 9 also marked by ø, or Ǹand class 10 by the prefix səor suffix -sə [START_REF] Tatang | Aspects of Kung grammar[END_REF]).

The only noun class marker that is a suffix in many of these languages is the class 10 suffixsí also found in several other Western Grassfields Bantu languages of the Ring subgroup, e.g. Vengo, Lamnso, etc. Hyman (1980b: 254) argues that …one of the characteristics of all of the Ring group except West Nkom is the *-sí suffix of class 10 … it probably originated as a device to make explicit the plurality of class 10 nouns. As such it is found only on class 10 nouns in isolation, or in constructions where the plurality would not be evident from surrounding forms.

It should be noted that -sí attaches in Babanki, Kom and Oku as a suffix while it is prefixed in Kuk and Mmen but can be either a prefix or suffix in Bum and Kung. It will be seen in §4 that, depending on the language, the tone of -sí can be realized H, ꜜH, M, L o (i.e. non-gliding final low) or L. The following table shows the noun classes and their affixes in Proto-Ring and in CRGL. Class 9/10 nouns fall into two categories in these languages with slightly more than half of the 1 The IPA symbols for the following orthographic symbols used in this paper are given in square brackets: ny

Class PR Babanki Bum Kom Kuk Kung Mmen Oku 1 *ù- Ø, Ǹ- Ø, (à) Ø, w- Ø- Ø- Ø, u- (ɛb-) 2 *bá- və- -á Ø, gh(e)-1 ʌ- ə- Ø, ʌ- (ɛ-) *kí- kə- à- a- kə- kə- a- ke- 8 *bí- ə- ù-, -ú e-( w ) u- ù- e--w - ɛb- 9 *Ǹ-,*Ø Ø, N- Ø, N-, (à)- Ø, N- Ø, N- Ø, N- Ø, N- Ø, N- 10 * ́...-sí -sə́sə-, -sú- Ø …-sé sə- sə-, -sə́ se- -sə1 3 *tə́tə- tə-, -tú- te- -- -- te- tə- 19 *fə́fə- fə- fe- fə- fə- fe-, fə- fə-
[ɲ], sh [ʃ], zh [ʒ], gh [ɣ], ch [tʃ], j [dʒ], y [j]. 2
The numbering in the first column is according to the Bleek-Meinhof reference system [START_REF] Katamba | Bantu nominal morphology[END_REF]. The Proto-Ring reconstructions in the second column are from Hyman (1980b: 251). Babanki data have been taken from [START_REF] Akumbu | A pedagogical grammar of Babanki[END_REF], Bum data from Hyman (1980b), Kom data from Hyman (2005), Kuk data from Kießling (in preparation), Kung data from [START_REF] Tatang | Aspects of Kung grammar[END_REF], Mmen data from [START_REF] Kießling | Infix genesis and incipient initial consonant mutations in some lesser known Benue-Congo languages[END_REF] and Oku data from Hyman (1980b) nouns beginning with a NC cluster e.g. Kom: ŋgvɨ̄ 'hen', ndòŋ 'potato', and njàm 0 , 'axe' while the rest lack this nasal: lòm 'dry season', káyn 'monkey', and gwén 'farm' (Hyman 2005: 315). In addition, "the identity of the nouns falling in one vs. the other category is relatively stable from language to language within WGB. Thus, 'dog', 'goat' and almost all other animals occur without a nasal, while non-animal 9/10 nouns such as 'axe', 'horn' and 'message' usual take a nasal (Hyman 1980a: 184)3 ." Synchronically, the nasal is considered to be part of the stem [START_REF] Akumbu | Nasals and low tone in Grassfields noun class prefixes[END_REF]. As it will be seen in the next section, the distinction between the two categories can be relevant because the nouns without a nasal sometimes behave differently from a tonal point of view than those with a nasal.

4. Class 9/10 tone CRGL distinguish two underlying tones, L(ow) and H(igh). On the surface, they have a level low tone (L o ) contrasting with the normal, falling L tone, but only before pause. In addition, a M(id)

tone occurs in all the languages while Babanki also has a downstep (ꜜH) entity. 4 Tonal alternations in class 9/10 in CRGL are pervasive and complex. A few phonological variations can also be spotted in class 1/2 in these languages, but it is possible to make generalizations about them, as in the following Babanki nouns that undergo segmental and/or tonal changes:

( Of the seven languages, only Kom has an identical tone on the stem in both classes in Table 2 whereas the tone of the class 10 affix is different from the underlying H in all the languages. 5

This reveals the pervasive nature of the tonal variations, some of which are further illustrated and discussed below.

Identical class 9/10 tone

The Central Ring language that shows the most correspondence between class 9/10 tones is Mmen. Apart from the three nouns found so far and mentioned below (7c) the rest have identical tones in the singular and plural:

( These data show that it is possible to have identical tones in class 9/10 stems in Central Ring Grassfields languages. However, as seen next, this is not always the case as a certain number of nouns exhibit tonal differences between the singular and plural forms in this gender.

Tonal variation in class 9/10 stems

There are stems that have a L tone in class 9 but a H tone in class 10, as seen in Babanki (7a), Kung (7b) and Mmen (7c) 6 :

( The change from root L tone in class 9 to H in class 10 shown in (7a-c) is clearly predictable from Proto-WGB. As pointed out by Akumbu & Hyman (2017: 8), "Class 9 was originally marked by a L tone prefix, while class 10 still shows the effects of an original H tone prefix. Synchronically, we can posit corresponding floating tones.'' In other words, positing a floating L tone before the singular and a floating H tone before the plural forms would account for the changes. As in Babanki (8), when the class 10 /H/ prefix associates to the /L/ root, the L delinks, conditioning the downstep on the suffix /-sə/:

(8) H tone grounding (HTG) in class 10

jɔm-sə [jɔḿꜜsə] = H L H
In Kung (7b) and Mmen (7c) the delinked L tone undergoes Stray Erasure [START_REF] Steriade | Greek prosodies and the nature of syllabification[END_REF][START_REF] Snider | The geometry and features of tone[END_REF] as it has no observable effect in the phonetics.

Certain L tone stems maintain the L in the plural but the H suffix becomes L o in Kom (9a) and Oku ( 9b Nouns like those in (20) might have had a H prefix which goes onto the root and creates a falling tone in the singular but delinks the L in the plural. As seen, the L that floats in the plural produces a M in these languages that have a general M tone [START_REF] Hyman | Floating tones in Mbam-Nkam[END_REF]. In Bum and Kung, the H prefix goes onto the root in both the singular and plural forms creating a falling tone:

(

Conclusion

Singular (class 9)/plural (class 10) tonal alternations are common in all Central Ring Grassfields languages although the behavior of the tones differs significantly from language to language. The discussion in this paper supports the reconstruction of L tone for class 9 and H tone for class 10 as the Proto-Grassfields singular/plural prefixes (Hyman 1980b: 252-254). In other words, positing a floating L tone before the singular and a floating H tone before the plural forms accounts for most of the cases. It is therefore evident that the floating tones that have resulted from the loss of the vowels of these prefixes are responsible for the observed tonal changes in the noun stems.

Table 1 :

 1 Noun class affixes in PR and Central Ring languages 2

Table 2 :

 2 The tendency is for the tone of the stems in (2) to be high in the plural class 2. The situation in class 9/10 is more complicated as shown in Table2where the tone of the plural form differs from that of the singular form in six of the seven languages. Realization of *nàm ̀ 'animal'[START_REF] Hyman | Index of Proto-Grassfields Bantu roots[END_REF]

	1)	sg. (class 1) pl. (class 2) gloss
		wìʔ	víʔí	'person(s)'
		wàyn	vúnə́	'child(ren)'
		chì	və-chí	'in-law(s)'
		tsɔŋ	və-tsɔŋ	'thief(ves)'
		A straightforward remark that can be made here is that the L tone of class 1 noun stems in
	(1) becomes H in class 2. Segmental and/or tonal alternations in class 1/2 are also seen in other
	CRGL as follows:
	(2)	a.	Oku:	wān	ghɔń	'child(ren)'
		b.	Mmen:	wùɔ̀	ghɨ́	'person(s)'
		c.	Kuk:	wù	ghɨ́	'person(s)'

  It is unclear why the floating H doesn't associate but the L spreads. A similar situation is found in Kuk where the floating H-fails to link and the L tone of the root is maintained in class 10:In class 10 the H prefix is deleted in Babanki by Stray Erasure since its grounding would have no effect. The presence of the nasal in the NC initial cluster in Oku prevents the H from linking (See Akumbu & Hyman 2017 for a discussion of the relationship between NC clusters and tone in While the other languages simplify their contour tones, Kuk allows one in this context. It is possible that these nouns are doubly prefixed by sə-and the floating prefixal H that merge and then spread onto the root L. While HTG results to L tone delinking, HTS results to a contour tone.High tone roots, on their part, cause downstep of the suffix H in class 10 as in Babanki (18a), or create a M tone as in Kom (18b) and Bum (18c):

	b. (13) LTG in class 9 Oku: (17) nyàm ghàm zùghù	njàm kà Babanki sə-nyâm 'animal(s)' njàm-sɨ̀o kà-sè o sə-ghâm 'mat(s)' bìŋ bìŋ-sè o shɨ [shɨ ̀o] sə-zûghù 'snake(s)'	'axe(s)' Oku 'basket(s)' 'rainy season(s)' njam [njàm o ]
				mbàn =	mbàn-sè o	'fence(s)' =
	Historically these nouns were *L and synchronically they can be analyzed as /L-L/ in class 9 and L H L H
	/H-L/ in class 10. Unlike in Babanki (as in 8 above), the floating H-prefix fails to link but the L
	spreads to the suffix, converting the H to L˚:
	(10) Low Tone Spread (LTS) in class 10 ka-sə (18) a. Babanki byí Grassfields Bantu) and the LH stem simplifies to L: byí-ꜜsə́ bʉ́ bʉ-ꜜsə́ [kà-sə̀o] (14) a. HTG in class 10 (Babanki) ndzɔŋ ndzɔŋ-ꜜsə́ b. b. Kom: dzɨ́ dzɨ́-sɨ̄ = H L H shɨ-sə [shɨ ́sə] bɨ́ bɨ́-sɨ̄ bzɨ́ bzɨ́-sɨ̄	'goat(s)' 'dog(s)' 'thorn(s)' LH simplification (Oku) 'road' njam-sə 'dog' [njàmsə] 'goat'
	c. H H H	Bum:		ājəŋ ānjáŋ	jəŋ-sə̄ njáŋ-sə̄	'hunger' = H LH H 'xylophone(s)'
				ājəḿ	jəḿ-sə̄	'back(s)'
	(11) ŋmgbàʔ High Tone Grounding is seen in Oku in certain stems that lack an NC initial cluster: sə-ŋmgbàʔ 'mountain(s)'
	tɔ̀ Downstep or M suggests that these nouns were *HL historically (e.g. Proto Bantu *búà 'dog'). sə-tɔ̀ 'pot(s)'
	ndzàm (15) kān Synchronically, they can be modeled as a linked H followed by a floating L which triggers either sə-ndzàm 'axe(s)' kán-sə́ 'monkey(s)'
	səə downstep of the suffix H (Snider 1999, Akumbu 2018) or lowers it to M: səə-sə́ 'fish(es)' On the other hand, the non-gliding L˚ roots which are historically *H can be analyzed as /L-H/ in class 9 and /H-H/ in class 10 in Babanki (12a) and in Oku (12b) they are analyzed as /L-kfən kfəń-sə́ 'hill(s)' (19) a. byi-sə [byíꜜsə ] b. dzɨ sɨ [dzɨ ́sɨ ̄]
	H/ in class 9 but /H-LH/ in class 10. In both languages the suffix remains H: The L-H in class 9 becomes M while the floating H-prefix of class 10 goes into the stem and
	(12) a. delinks the L which is eventually deleted by Stray Erasure: Babanki: shɨ̀o shɨ́-sə́ HL H	'hoe(s)' HL H
	zhʉ̀o nyì o njàm o Finally, a falling tone in the stem of class 9 nouns becomes H in class 10 and the H suffix is zhʉ-sə́ 'bee(s)' nyí-sə́ 'machete(s)' b. Oku: njàm-sə́ 'axe(s)' (16) HTG in class 10 (Oku) M as in Oku (20a) and Kom (20b):
		kan-sə	ŋkfʊ̀o [kánsə]	ŋkfʊ-sé	'rope(s)'
	): (20) a.	Oku: =		ntɛk o fê nûŋ	ntɛk-sə́ fé-sē núŋ-sē	'hoe(s)' 'quarter(s)' 'hair(s)'
	The L prefix (of class 9) docks onto the root and delinks the H which floats and prevents the L H LH H nyâm nyám-sē 'animal(s)'
	(9) from gliding: a. b.	Kom: Kom:		bò jɨ̂m	bò-sɨ̀o jɨ́m-sɨ̄	'bag(s)' 'back(s)'
	bèŋ A slightly different outcome is found in Kuk where HTG results to a contour tone on /H-L/ bèŋ-sɨ̀o 'rainy season(s)' kû kú-sɨ̄ 'nut(s)' stems in class 10: nyûŋ nyúŋ-sɨ̄ 'hair(s)'

6

The noun roots in this category lack an initial NC and all begin with a simple consonant.

  The grounding of the H tone to produce a falling tone in Bum and Kung is modeled as follows:

	21) a.	Bum:	nyâm	sə-nyâm	'animal(s)'
				nyûŋ	sə-nyûŋ	'hair(s)'
				bvû	sə-bvû	'goat(s)'
		b.	Kung:	ífû	sə-fû	'leaf(ves)'
				ínyûŋ	sə-nyûŋ	'hair(s)'
	(22)	a.	HTG in class 9		b.	HTG in class 10
		nyam	[nyâm]		sə-nyam [sə-nyâm]
		H L				L H L

*ú-əù-e-( w ) u-ù-e--wɛb-4 *í-----i-i---e-(i-) 5 *í-əì-i-i-ì-e-i-6 *á-à-à-, -á a-ʌ-ə-ʌ-ɛ-6a *mə-mə-m̀-, -mú me-m-m-m-m-

As pointed out byHyman (1980a: 14), "a homorganic nasal is sometimes found on a few nouns sporadically in other classes, but nowhere near the frequency with which it is found on 9/10 nouns".

See Akumbu (2018) for a discussion of M and ꜜH in Babanki.