Pierre-Antoine Arrighi

Santosh Maurya

Céline Mougenot

Towards Co-designing with Users: A Mixed Reality Tool for Kansei Engineering

Keywords: customer requirements, collaborative design, mixed reality, kansei engineering, tangible user interfaces

Some costly and complex technical products, such as walking assistance devices, require ad-hoc design processes to address the very specific needs of each user. However, the depiction of customer/user requirements in the early stage of design stands difficult due to their subjective nature and the separation between the user and the designer. To bridge these gaps, we introduce the definition of a new modular digital toolbox based upon mixed reality system and kansei engineering techniques. The hardware consists in modular Tangible User Interfaces (TUIs), custom made by 3D printing and powered by a 3D game engine. The interactive content is displayed in mixed reality, simultaneously to the user and the designer. Kansei data are collected through questionnaires and psychophysical measurements, during multiple collaboration phases. The modularity of the system allows the evaluation of various TUIs, 3D content behaviours and the best fitting type of display.

1

Introduction and motivation

Supporting mobility requires the design of complex mechanical products

We are currently in the midst of a profound demographic shift. The aging of the population in developed countries is a groundswell, due to a slowing birth rate and an increasing life expectancy. In Japan for example, the share of the population over 60 was 8% in 1950, 10% in 2000, and is expected to reach 21% in 2050. In a near future, one out of four people will be over 65 [START_REF] Nagamachi | Innovations of Kansei engineering[END_REF]. Among all challenges raised by the aging of the population, mobility appears as one of the most pressing issues [START_REF] Metz | Mobility of older people and their quality of life[END_REF]. The prevalence of mobility impairments increases with age, i.e. one in ten for people in their fifties, up to one in two for those in their eighties. Losing complete or partial mobility affects not only the ability to walk, but also the ability to perform daily tasks, which is a major determinant in quality of life and causes dependence on others [START_REF] Martins | Assistive mobility devices focusing on smart walkers: classification and review[END_REF]. To address walking disabilities, "one fits all" solutions are the most common. As an example, wheelchairs are often recommended to patients with mobility impairment conditions caused by lower limbs disability. Although safe and easy-to-use, they also have many disadvantages, e.g. they limit activities due to their large footprint and make it complicated to perform basic daily tasks due to the limited reach they offer.

Wheelchairs also tend to limit the visibility field of their users, making it difficult both to see and to be seen.

In order to overcome most of these limitations, efforts have been put to offer users an upright posture through more sophisticated products. For instance, robotic exoskeletal apparatuses [START_REF] Martins | Assistive mobility devices focusing on smart walkers: classification and review[END_REF] such as powered suit HAL [START_REF] Farris | Preliminary evaluation of a powered lower limb orthosis to aid walking in paraplegic individuals[END_REF], Ekso [START_REF] Strickland | Good-bye, wheelchair[END_REF] or Vanderbilt Powered Orthosis [START_REF] Farris | Preliminary evaluation of a powered lower limb orthosis to aid walking in paraplegic individuals[END_REF][START_REF] Quintero | A method for the autonomous control of lower limb exoskeletons for persons with paraplegia[END_REF]. Some of them may require using an additional remote walker [START_REF] Kong | Design and control of an exoskeleton for the elderly and patients[END_REF]. However, such products tend to be complicated and expensive, both to design and operate.

New design tools for a better fit to user requirements

For designers, one way of simplifying their products is to take into account the fact that many people with walking-impairment have a valid upper body. Therefore, the focus of research has shifted towards apparatuses capable of autonomously supporting users by leveraging their remaining upper mobility and led to the design of simpler and less expensive devices like illustrated in Fig. 1 (c) [START_REF] Matsuura | Efficiency improvement of walking assist machine using crutches based on gait-feasible region analysis[END_REF][START_REF] Higuchi | Development of a walking assist machine using crutches (Composition and basic experiments)[END_REF]. Due to space limitations, we are not able to give more details about our use case. At the same time, quality of living and comfort has taken priority over simple functional solutions for the users. In projects involving medical assistance devices, it is of paramount importance to take into account the detailed condition of the user and focus on ergonomics, usability, user acceptance, body metrics and adequacy to the user's feeling [START_REF] Farris | Preliminary evaluation of a powered lower limb orthosis to aid walking in paraplegic individuals[END_REF]. Focusing on such items can result in safer products and faster learning curves for the user [START_REF] Martin | Medical device development: The challenge for ergonomics[END_REF]. These elements are key drivers of the final product properties and should be considered from the very early design stages. They are all related to what is called the user 'kansei' [START_REF] Nagamachi | Kansei/affective engineering[END_REF]. Kansei is a Japanese term that can be translated as "emotion" or "affect" and encompasses all aforementioned items. It is deeply linked to the customer requirements; as kansei engineered products tend to increase the satisfaction of their users. However, incorporating the kansei requirements at early design steps poses a major challenge because designers need to take into account both psychological and physiological user requirements simultaneously.

Hence our research question: How to improve the design process of products that require a good fit with user requirements, such as walking assistance devices?

Early user involvement in the design process has several advantages. The main benefits are an increased access to and understanding of the user's needs, experiences, and ideas; improvements in medical devices designs and user interfaces; and an increase in the functionality, usability, and quality of these devices. In particular, the involvement of users is crucial at each stage of the product development cycle to leverage in a cumulative way their contributions and thus to maximize their effects [START_REF] Shah | Benefits of and barriers to involving users in medical device technology development and evaluation[END_REF]. One good option for integration through collaboration between user and designer during the design process is the use of common "tools". The tools are able to trace the interactions between users, they support the design process itself and produce representations of the concept, from early steps to final completion of the physical object. The representations are key for collecting one's kansei [START_REF] Nagamachi | Kansei/affective engineering[END_REF] and can be used as boundary objects [START_REF] Carlile | A pragmatic view of knowledge and boundaries: Boundary objects in new product development[END_REF]. The tools facilitate exchange between the designers and the people who will experience the products [START_REF] Sanders | From user-centered to participatory design approaches[END_REF].

Therefore our objective is to invent a new tool to support the integration of the user and their kansei requirements inside the design process of medical assisting walking devices. For an optimal integration and compatibility into the current digital design process of such products we concentrated our research on Computer Aided Design (CAD) tools.

Hypothesis: With an earlier involvement of the user in the design process it is possible to design better products. This could be achieved with a new tool that allows the user to participate in the early stages of the design process the mobilization of his kansei data can leverage the design process for better products.

2

Existing digital design tools and methods

CAD strength and weakness in early design stage

The design of most complicated devices requires simulations, analysis, and optimisation conducted with CAD tools. As a consequence they are essential when dealing with the design of medical assistance devices. However, the participation of users during the design process and the integration of kansei engineering from the early steps could be improved.

Because of the number of functions they support the CAD tools require a long training with steep learning curves. The designers who use them only become experts after years of mechanical education. They require good perceptive and imaginative skills along with a technical educational background [START_REF] Hamade | A study of the influence of technical attributes of beginner CAD users on their performance[END_REF]. Their complexity notably lies in their human machine interfaces, which impair collaboration and direct interaction with the CAD objects [START_REF] Sidharta | Augmented tangible interfaces for product assembly planning[END_REF]. The keyboard and mouse widely dominate work environments. If they are very capable in terms of performance in expert's hands they however might not be easy to handle by elderly people who are sometimes unfamiliar with the technology. They also require dexterity and precision, which may be an issue in the case of physical impairment.

The compatibility of CAD tools with early design stages, when kansei requirements must be generated and collected, could also be improved. The conceptual design phase is critical for involving collaboration between designers and users and integrating the specific requirements of the latter [START_REF] Wang | Collaborative conceptual design -state of the art and future trends[END_REF]. As a consequence, the user is often requested to give feedbacks about already well-developed representations (e.g. CAD models), which are difficult to interact with. Recently, new types of Computer-aided Design interfaces can produce realistic representations of the product being designed for a reasonable cost. The Fig. 2 illustrates the limited feedbacks and perception clues for a user. Mixed Reality (MR) is defined as a particular subset of Virtual Reality (VR), related technologies that involve the merging of real and virtual worlds somewhere along the "virtuality continuum" [START_REF] Milgram | A taxonomy of mixed reality visual displays[END_REF] that spans between completely real environments and completely virtual ones and illustrated in Fig. 3. One of the major advantages of this type of interfaces is the possibility of leveraging the real world with virtual elements (as in augmented reality) or to map virtual elements to real physical objects manipulated by the user (as in augmented virtuality).

Fig. 3.

The "virtuality continuum" as defined in [START_REF] Milgram | A taxonomy of mixed reality visual displays[END_REF].

MR systems can facilitate the integration of user in the design process because they offer an enhanced perception of the future product. The VR technology enables the user to experience the design model with high quality of presence by using the interactive three-dimensional image without making an actual product from the early design stages [START_REF] Ogi | Education on Human Centered Design Using Virtual Environment[END_REF]. They offer shared representations and boundary objects for better communication between designers and users. Boundary objects [START_REF] Carlile | A pragmatic view of knowledge and boundaries: Boundary objects in new product development[END_REF] work to establish a shared context between designers. They can be objects or models are simple or complex representations that can be observed and then used across different functional settings. These representations of the under design object depict or demonstrate current or the possible "form, fit, and function", in other words, fitting to the knowledge of the user. An enhanced perception of the CAD object for the user is illustrated in Fig. 4.

Kansei engineering methods for early incorporation of user preference

Kansei engineering is a technique that can contribute to higher user satisfaction [START_REF] Nagamachi | Kansei/affective engineering[END_REF]. However, its implementation in real life is difficult, especially when the products to be designed are complex and when the design is done in a lab-based environment, as is it the case for walking assistance devices.

Design engineers have their own tools, processes and methods [START_REF] Arrighi | Addressing constraints creatively: how new design software helps solve the dilemma of originality and feasibility[END_REF]. In order to capture the user requirements during the medical design solution development, designers usually refer to existing references. However, the methods discussed in the scientific literature can rarely be applied to actual use cases, while current industrial practice may be confidential, and there is little knowledge available about methods and approaches needed to capture the full range of requirements [START_REF] Martin | Medical device development: The challenge for ergonomics[END_REF]. Designing specific walking assistance devices implies the collection of all the specific requirements from the end user. It is expected from the designers to know the kansei and lifestyle of users and to suggest realistic solutions to improve them [START_REF] Nagamachi | Innovations of Kansei engineering[END_REF]. The kansei requirements challenges come on top of the traditional technical challenges, which are already demanding and labour intensive [START_REF] Martin | Medical device development: The challenge for ergonomics[END_REF].

This leads to the interweaving of several academic fields, i.e. medicine, engineering and social sciences [START_REF] Sankai | HAL: Hybrid assistive limb based on cybernics[END_REF]. As a consequence kansei engineering design often imply the integration of dedicated kansei tools and methods in addition to the process [START_REF] Nagamachi | Kansei engineering as a powerful consumer-oriented technology for product development[END_REF][START_REF] Nagamachi | Kansei/affective engineering[END_REF]. However this approach consider the user as a source of design information but mostly as an indirect participant. Kansei engineering methods recommends the collection of customer feedbacks at the early design steps for best results. Measurable usability criteria address issues related to the effectiveness, efficiency, safety, utility, learnability and memorability.

We want to mix the advantages of MR (virtual and augmented reality tools with Tangible User Interfaces (TUIs) with kansei engineering techniques. Successful projects have been conducted with the integration of VR and kansei engineering, as schematised in Fig. 5. This technique is called kansei engineering type IV [START_REF] Nagamachi | Innovations of Kansei engineering[END_REF].

Co-design for user early involvement

Typical digital tools follow a step-by-step process where representations are first shown to the user and then modified by the designer, as illustrated in Fig. 6. This step by step process requires the designer involvement to modify the CAD object after collecting the user's feedbacks. Collaboration and co-design imply the ability for all participants to be able to modify and interact directly with the representations, as illustrated in Fig. 7. Doing so in a digital environment implies dedicated tools capable of supporting such activities, with specific interfaces. This requirement is even more stringent when dealing with the early design steps.

Definition of a new MR kansei based tool for early co-design

Principles of the tool

The tool needs to be compatible with the current design process, namely the digital tools the designers are already using and their methods. We will use digital tools and the manipulation of CAD data for a better integration. The system will focus on the initial design steps for the definition of user requirements and during the design iterations and evaluations of digital prototypes.

The tool needs to integrate the user in the design process by giving him/her simple interfaces to collaborate actively with the designers. We also need the system to be capable of changing configurations for fitting different users. One of the solutions is to create the interfaces on demand for each use case and ensure their compatibility with the system with a modular architecture.

The tool needs to be kansei-engineering compliant. A kansei engineering process requires being written in addition to the already existing design process, and capable of leveraging the capacity for the designers to capture kansei data through interaction/collaboration phases with the user. The Fig. 8 illustrate this workflow. The Kansei data will be generated by a mix of several techniques, listed in Table . 1. During the design process, the psychophysical state of the user is evaluated. His/her satisfaction is eventually assessed through a questionnaire. The design tool itself is also rated with the Self Assessment Manikin (SAM) method [START_REF] Bradley | Measuring emotion: the self-assessment manikin and the semantic differential[END_REF].

Kansei data Assessment Method

Usability / User Satisfaction -Questionnaire Emotional reaction (valence, arousal and dominance) -Self Assessment Manikin -Psycho-physical measurements (heart beat frequency, face expression recognition, skin conductance)

3.2

Originality and expected benefits Our tool offers three major advantages and combines the advantages of existing methods and techniques. We build on demand the TUIs, ad-hoc to each new product development. 3D printing seamlessly integrates with CAD and has the ability to produce custom interfaces at relatively low prices. The tool offers rich interactions with touch, vision and hearing senses. TUIs can mimic real world environment and be very effective for users both experts and not experts of digital design environments, they can be effective boundary object and media of communication and collaboration. The possibility to observe and collect more accurately the expressed feelings and intentions of the participants is also increased. Tangible Augmented Reality (AR) combines the intuitiveness of TUIs with the enhanced display possibilities afforded by VR. This allows the implication of the user during the early design stages [START_REF] Billinghurst | Experiments with faceto-face collaborative AR interfaces[END_REF]. The benefits of TUIs include allowing multiple users to simultaneously view, feel and manipulate a physical shape instead of an abstract graphical representation [START_REF] Leithinger | Direct and gestural interaction with relief: a 2.5 D shape display[END_REF]. TUIs also bridges the gap between the worlds of bits and atoms through graspable objects and ambient media in physical environment [START_REF] Ishii | Tangible bits: towards seamless interfaces between people, bits and atoms[END_REF].

Description of the system

The full system we experimented is schematized in Fig. 9. Easy-to-use hardware.

The Oculus Rift® is a cheap head mounted display with an average price tag of USD 300. It is capable of delivering stereoscopic images using a low persistence OLED screen to eliminate motion blur and judder. Low persistence makes the scene appear visually stable, increasing the potential for presence. It is installed with an additional positional tracking and can accurately map all of the user's head movements. We 3D print TUIs on demand for each project so they can be fitting to both the project and the user who will collaborate to the design process. The 3D printed interfaces are made from simplified shapes of the early design subcomponents of the product as recommended in kansei engineering methods. The 3D printed TUIs are produced ad-hoc to be simultaneously easy to manipulate and track. They are produced with a Keyence® Agilista 3100 3D printer. We use the Microsoft Kinect® for 3D tracking them.

The software implementation offers modularity. Unity® is a flexible development platform for creating multiplatform 3D and 2D games and interactive experiences. We use it to connect the TUIs to the virtual objects of the 3D scene to the stereoscopic display. With Unity® software it is possible to assign to each TUIs several behaviours depending on the specific design task and the user.

Conclusion

By combining mixed reality tools and tangible user interfaces, we created a new computer-aided design system which facilitates the design collaboration between designers and users and which allows to collect user data / kansei data in the early designs stage.

Our work will now focus on implementing and testing the tool in the context of a real-life design of new WAMC. In complement of the kansei data generated by the user, the usage of the tool from the design engineers' point of view will be assessed. i.e. how useful is the user generated data and the productivity of the collaboration. The development of such a co-design digital tool is expected to help engineers designing user-friendlier products. This could enhance the quality of life for people through better user experiences with their goods.

Fig. 1 .

 1 Fig. 1. Illustration of assistance devices for walking impaired people. (a) bimanual rear-wheel driven folding wheelchair, (b) Exoskeleton (HAL) [4], (c) Walking assist machine using crutches (WAMC) [8].

Fig. 2 .

 2 Fig. 2. Integration of the user in the design process with CAD tools.

Fig. 4 .

 4 Fig. 4. Integration of the User in the design process with VR CAD tools.

Fig. 5 .

 5 Fig. 5. Integration of the User in the design process with VR CAD tools in kansei engineering type IV [1].

Fig. 6 .

 6 Fig. 6. Flow of representations along the design process.

Fig. 7 .

 7 Fig. 7. Flow of representations along a co-design process.

Fig. 8 .

 8 Fig. 8. Co-design between Designer and Co-design with Designer and User with the combination of MR system and kansei engineering IV [1].

Fig. 9 .

 9 Fig. 9. Schematic description of the system.

Table . 1

 . . Items collected for creating the kansei data and the associated methods.

Acknowledgements

This research has been funded by the Japan Science and Technology Agency (JST) Start-up Grant for Tenure-track Researchers, Number KH26000802.


Thorsten Wuest
email: thwuest@mail.wvu.edu

Stefan Wellsandt

Klaus-Dieter Thoben

Information Quality in PLM: A production process perspective

Keywords: Product Lifecycle Management, quality management, manufacturing, production, production planning and control, data quality

Recent approaches for Product Lifecycle Management (PLM) aim for the efficient utilization of the available product information. A reason for this is that the amount of information is growing, due to the increasing complexity of products, and concurrent, collaborative processes along the lifecycle. Additional information flows are continuously explored by industry and academia -a recent example is the backflow of information from the usage phase. The large amount of information, that has to be handled by companies nowadays and even more in the future, makes it important to separate the "fitting" from the "unfitting" information. A way to distinguish both is to explore the quality of the information, in order to find those information that are "fit for purpose" (information quality). Since the amount of information is so large and the processes along the lifecycle are diverse in terms of their expectations about the information, the problem is similar to finding a needle in a hay stack. This paper is one of two papers aiming to address this problem by giving examples why information quality matters in PLM. It focuses on one particular lifecycle process, in this case production. An existing approach, describing information quality by 15 dimensions, is applied to the selected production process.

Introduction and problem description

Closing the information loops along the product lifecycle is a recent effort undertaken by research projects [START_REF]Manutelligence project[END_REF], [START_REF]Falcon project[END_REF]. One of the reasons why closing information loops is so important is the expectation that activities like design, production, sales and maintenance will be able to realize products and services with a better ratio between expected and delivered characteristics (i.e. higher quality). As product quality is di-rectly influenced by the quality of the production processes [START_REF] Brinksmeier | Prozeß-und Werkstückqualität in der Feinbearbeitung[END_REF][START_REF] Jacob | Qualitätsmanagement und Normung[END_REF], an increased availability of information will benefit production planning and control activities. Additional information can help to understand complex problems and take the most suitable decisions to address them in a timely manner -common examples for these benefits are Concurrent Engineering [START_REF] Fohn | Concurrent engineering[END_REF] and agile software development [START_REF] Highsmith | Agile software development: the business of innovation[END_REF].

Technical capabilities for the collection and analysis of information, as well as a sound business case are important prerequisites to increase the availability of information in decision-making. However, the growing amount and heterogeneity of information caused by, e.g. the industrial Internet and the Internet of Things, foster the need to identify information that is fit-for-purpose (i.e. focus on information quality). Recent literature about PLM puts little emphasis on this aspect. This paper will discuss the importance of information quality in PLM from the perspective of production. The same issue but from a product design perspective is described in a sister paper (see [START_REF] Wellsandt | Information Quality in PLM: A Product Design Perspective[END_REF]). Section two of this paper outlines information flows in PLM and an exemplary approach to describe information quality.

2

Related work

Information flows in PLM

Handling product data and information along the complete product lifecycle is stated as PLM [START_REF] Kiritsis | Closed-loop PLM for intelligent products in the era of the Internet of things[END_REF]. A product's lifecycle can be structured into three subsequent phases stated as 'beginning of life' (BOL), 'middle of life' (MOL) and 'end of life' (EOL). The initial concept of PLM was extended during the EU-funded large-scale research project PROMISE -it demonstrated the possibilities of closing information loops among different processes of the lifecycle [START_REF]Promise Integrated Project[END_REF]. The recent concept of PLM is illustrated in Figure 1. Internal information flows within the phases are not covered in the illustration.

Fig. 1. A product lifecycle model and its major information flows [START_REF] Wellsandt | Sources and characteristics of information about product use[END_REF] Among the three lifecycle phases, at least two types of information flows can be established. The forward-directed flows are the ones that are typically mandatory to design, produce, service and dismiss the product. Backwards-directed flows are typically optional and allow optimization of processes/activities.

Information Quality (IQ)

Seamless decision-making processes are largely based on high-quality information. Decision-makers realize issues with information quality if their expectations about the information are not met. Examples for potential problems caused by low information quality are summarized in Table 1.

Table 1. Examples of problems related to flawed information [START_REF] Ge | A Review of Information Quality Research -Develop a Research Agenda[END_REF] not based on fact consists of inconsistent meanings is irrelevant to the work of doubtful credibility is incomplete is hard to manipulate presents an impartial view is hard to understand -From a general perspective, the quality of information can be defined as the degree that the characteristics of specific information meet the requirements of the information user (derived from ISO 9000:2005 [START_REF]Quality management systems -Fundamentals and vocabulary[END_REF]). Since the topic is intensely discussed for at least two decades, several sophisticated definitions for 'information quality' exist. Since the purpose of this paper is not to discuss these fundamental concepts, a thoroughly discussed definition is selected for this paper. Rohweder et al. propose a framework for information quality that is an extension of the work conducted by Wang and Strong [START_REF] Wang | Beyond Accuracy: What Data Quality Means to Data Consumers[END_REF] -the framework contains 15 information quality dimensions that are assigned to four categories as summarized in Table 2. The selected definition of information quality contains four categories of dimensions that are related to a specific scope. Each category has dimensions that characterize information by two to five dimensions (15 in total). A brief description of some dimensions is provided in Table 3.

Table 3. Excerpt of quality dimensions and their description (based on [14])

Quality dimension Description

Reputation Credibility of information from the information user's perspective In order to receive a specific statement about the actual quality of an information item, the as-is characteristics of the item must be compared with the required characteristics (preferably using all of the quality dimensions). The better the matching is, the higher the information quality is considered.

Approach

Production is the process of realizing products according to the specifications originating from product development. In this paper, production includes production planning, manufacturing and assembly processes. During production, several characteristics of the later product and its behavior during usage are defined, e.g. by the chosen materials, machines and machine parameters. The decision of which materials, machines and parameters are going to be used is taken during the production planning phase and the previous product development phase. In this paper, the product development phase is not in the focus.

During production, information between different manufacturing processes is exchanged. The exchanged information is highly important to ensure the final product quality [START_REF] Wuest | Identifying Product and Process State Drivers in Manufacturing Systems Using Supervised Machine Learning[END_REF]. In manufacturing, especially in the area of process monitoring and control, information quality can play a decisive role in whether an analysis and the subsequent action is successful or not. In order to apply the selected quality dimensions to production, relevant information flows are divided into three categories as illustrated in Fig. 2.

Fig. 2. Types of information flows in production

Information flows within production (internal). In production, information quality is generally of very high relevance as it often has a direct impact on key figures of a company or a production network. Information used in manufacturing is often used as input for machines with a low level of robustness against, e.g., missing values. Today, production involves multiple processes exchanging not only physical goods but also information. Those process chains can become rather complex and can be considered dynamic. Looking at manufacturing at a more granular level, each process and product has to be considered individually due to, e.g., deviations in its materials.

Fig. 3. Internal information flows of a production process chain

Through the backflow of information about the individual product earlier in the same process or from previous processes individual adjustment of process parameters becomes possible. These adaptions of the process may lead to significantly improved performance and/or avoidance of significant problems. Today, many decisions regarding value adding production processes are taken based on available information. Control loops, scheduling decisions and program planning are just some examples which strongly depend on information quality. Information in this context can include realtime sensor information, e.g., for monitoring and control purposes, as well as quality measures for subsequent process adjustments. A practical example can be information about the individual chemical composition of the steel, used during heat treatment. This information is vital for reaching the quality goal.

Information flows towards production (inbound). Extending this towards the potential use of information from lifecycle phases other than production to support production processes in a similar way, certain differences come to mind and present specific requirements towards the information quality. The two main inbound information sources are depicted in Fig. 4.: 1) information from the product design phase and 2) information from the usage and maintenance phase.

Fig. 4. Inbound information flows towards production

The product design phase is essential for production. In design the main properties of the later product are set and the processes and process parameters are chosen according to the information received from design. For information from usage, there are two possibilities. First, the information is directly transferred and utilized or the usage information is indirectly utilized via the design phase. An example for relevant information from usage/maintenance is the surface quality of a product that depends on environmental factors during usage. A product's surface characteristics can be influenced to some extend during the production process (e.g., heat treatment).

Information flows from production (outbound). In production, information is not only utilized but also produced in large quantities -machinery and tools are equipped with sensors continuously producing information. Also process monitoring and advanced systems, like Manufacturing Execution Systems, contribute to the increased information generation. This information may be a valuable source for stakeholders outside of production. In Fig. 5., outbound information flows to three other lifecycle phases are depicted: 1) recycling and disposal, 2) usage and maintenance and 3) product design and development. Examples cases for these three information flows are:

1. Information about potentially hazardous materials of the product introduced during production (e.g. heavy metals). 2. Information about lubricants used during production which could influence the areas of application of the product (e.g. regulation in food processing industry). 3. Information can be directly utilized for future design improvements that lead to a variety of improvements, e.g. quality, efficiency or safety.

From the perspective of production, the example number three can be considered as the most important outbound information flow. Popular approaches like 'Design for Manufacturing' actually rely on such outbound information from production.

Fig. 5. Outbound information flows from production

Within all these different possible information flows, an important aspect to consider is the information quality. Whereas the right information in the right quality may lead to significant improvements, flawed information may even have a worse impact than no information at all. In the next section, this is discussed according to the previously introduced IQ dimensions.

Discussion

In this section, the feasibility of the different IQ dimensions during application in manufacturing and production planning is discussed. The overall structure follows the one depicted in table 2, with sub-sections resembling the four 'scope' categories. As mentioned, production is very diverse in the applied processes and also individual for each product type. Therefore, the given examples used to emphasize certain quality aspects are not meant to be comprehensive -there are, most likely, multiple other influences and aspects that are not covered in this paper. For each scope of the selected IQ framework, the three different information flows introduced in the previous section (i.e. internal, inbound and outbound) are briefly discussed.

Content scope

The content scope, resembling the IQ dimensions 'reputation', 'free of error', 'objectivity' and 'believability', is very relevant in production. For information flows within production (internal), 'free of error' is very important as the information is often directly utilized by technical systems. Given that process chains are often distributed between different locations and companies, 'reputation' and 'believability' may also be relevant. However, 'objectivity' may be considered less relevant in this area as measuring and sensor data can be considered rather objective by nature. For outbound and inbound information however, all four IQ dimensions are highly relevant. From a production perspective, these IQ dimensions matter most for inbound information. However, for other stakeholders within the product lifecycle, the importance of information quality of outbound information can be considered equally high. Here 'objectivity' is also relevant as these information items may contain human-authored feedback information including its characteristic of subjectivity -also stated as response-bias [START_REF] Wuest | Identifying Product and Process State Drivers in Manufacturing Systems Using Supervised Machine Learning[END_REF].

Appearance scope

The relevant IQ dimensions of this scope are 'understandability', 'interpretability', 'concise representation' and 'consistent representation'. For information flows within production (internal), all four IQ dimensions discussed here are important. In highly automated production environments, the appearance of information is mostly defined, due to standardization or design of the production system itself. If standards are not met nor the communication rules of the automated system are not followed, the system will fail in most cases. Thus, these IQ dimensions are hard requirements, which have to be fulfilled. In production processes with more manual work and thus more human-based decision-making, the appearance of information is less regulated and, therefore, must be controlled more. For inbound and outbound information flows, these IQ dimensions cannot be assumed fulfilled due to standardization. There, the information is more diverse and the possibility of different systems and/or requirements is rather high. Thus, these IQ dimensions have to be carefully considered prior to establishing collaboration along the product lifecycle.

Use scope

Regarding the use scope, the IQ dimensions 'timeliness', 'value-added', 'completeness', 'appropriate amount of data' and 'relevancy' are in the focus. Within pro-duction (internal) it can be observed, that timeliness, completeness, appropriate amount of data, and relevancy are highly important. The often-automated use of information by machinery and monitoring tools relies on information fulfilling these requirements. For instance, even though today's computing power and algorithms can handle large amounts of data rather well, it is still important to evaluate what data is really relevant with the goal in mind. For inbound and outbound information flows in production these factors are also of relevance, however, there the potential use is broader and thus the variety of quality requirements acceptable may be higher. For all information flows in production the IQ dimensions 'value-added' is very important, as it is after-all a business operation.

System scope

From a system perspective, 'accessibility' and 'ease of manipulation' are the desired IQ dimensions. Within production (internal), accessibility is critical, especially in distributed production environments. Assuming that in production information is mostly based on sensor or other non-human-authored data, the access is mostly depending on a) available communication means (technical) and b) the access rights. Ease of manipulation is on the other hand not considered critical within production. Regarding inbound and outbound information flows, accessibility is again highly critical, with access rights being rather complicated to manage. Ease of manipulation is more important here, as it might be necessary to reformat or pre-process information for different purposes.

Conclusion and Outlook

This paper discusses the importance of information quality in PLM from a production process perspective. From literature, a framework with 15 IQ dimensions is selected. Then three different categories of information flows are defined to structure the discussion. These flows concern the usage of information within production (internal), coming from production used elsewhere (outbound) and coming towards production form different phases (inbound). In the following discussion, the importance of information quality in production is discussed by mapping the IQ dimensions with the three types of information flows identified before.

While the depth of the investigation conducted in this paper remains rather low (e.g. few examples and no consistent use case), it aims to substantiate a debate about the importance of information quality in PLM. This topic is of major importance, as the amount, heterogeneity and velocity of available information is growing and the selection of relevant information becomes more difficult. The definition of three types of information flows (i.e. internal, inbound and outbound) can be applied to other processes along the product lifecycle, in order to receive examples for all major lifecycle phases. In future work, a combined paper is envisaged for that purpose.

Table 2 .

 2 Dimensions of information quality[START_REF] Rohweder | Informationsqualität -Definitionen, Dimensionen und Begriffe[END_REF]

	Quality category	Scope	Quality dimensions
	Inherent	Content	Reputation; free of error; objectivity; believability
	Representation	Appearance Understandability; interpretability; concise representation;
			consistent representation
	Purpose-dependent	Use	Timeliness; value-added; completeness; appropriate amount of
			data; relevancy
	System support	System	Accessibility; Ease of Manipulation

Acknowledgement

This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement no. 636951 (Manutelligence) and grant agreement no. 636868 (Falcon). The authors wish to acknowledge the Commission and all the project partners for a fruitful collaboration. Finally, the authors would like to thank the reviewers for their comments that helped to improve the manuscript.


Eriká H Abrahám

John Abbott

Bernd Becker

Anna M Bigatti

Martin M Brain

Bruno Buchberger

Alessandro Cimatti

James H Davenport

Matthew M England

Pascal Fontaine

John Abrahám

Bernd Abbott

Anna Becker

Erika Ábrahám

Stephen Forrest

Alberto Griggio

Daniel Kroening

Werner M Seiler

Thomas Sturm

SC 2 : Satisfiability Checking meets Symbolic Computation (Project Paper)

Keywords: Logical Problems, Symbolic Computation, Computer Algebra Systems, Satisfiability Checking, Satisfiability Modulo Theories

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The use of advanced methods to solve practical and industrially relevant problems by computers has a long history. While it is customary to think that "computers are getting faster" (and indeed, they were, and are still getting more powerful in terms of multicores etc.), the progress in algorithms and software has been even greater. One of the leaders in the field of linear and mixed integer programming points out [9, slide 37] that you would be over 400 times better off running today's algorithms and software on a 1991 computer than you would running 1991 software on today's computer. The practice is heavily inspired by the theory: [9, slide 31] shows that the biggest version-on-version performance advance in software was caused by "mining the theory". But this progress has been in what is, mathematically, quite a limited domain: that of linear programming, possibly where some of the variables are integer-valued.

There has been also much progress in the use of computers to solve hard non-linear algebraic 14 problems. This is the area generally called Symbolic Computation (or Computer Algebra). It includes solving non-linear problems over both the real and complex numbers, though generally with very different techniques. This has produced many new applications and surprising developments: in an area everyone believed was solved, non-linear solving over the reals (using cylindrical algebraic decomposition -CAD) has recently found a new algorithm for computing square roots [START_REF] Eraşcu | Synthesis of optimal numerical algorithms using real quantifier elimination (Case study: Square root computation)[END_REF]. CAD is another area where practice is (sometimes) well ahead of theory: the theory [START_REF] Brown | The complexity of quantifier elimination and cylindrical algebraic decomposition[END_REF][START_REF] Davenport | Real quantifier elimination is doubly exponential[END_REF] states that the complexity is doubly exponential in the number of variables, but useful problems can still be solved in practice ([3] points out that CAD is the most significant engine in the "Todai robot" project).

Independently and contemporaneously, there has been a lot of practical progress in solving the SAT problem, i.e., checking the satisfiability of logical problems over the Boolean domain. The SAT problem is known to be NPcomplete [START_REF] Cook | The complexity of theorem-proving procedures[END_REF]. Nevertheless, the Satisfiability Checking [START_REF] Biere | Handbook of Satisfiability[END_REF] community has developed SAT solvers which can successfully handle inputs with millions of Boolean variables. Among other industrial applications, these tools are now at the heart of many techniques for verification and security of computer systems.

Driven by this success, big efforts were made to enrich propositional SATsolving with solver modules for different theories. Highly interesting techniques were implemented in SAT-modulo-theories (SMT) solvers [START_REF] Barrett | Satisfiability modulo theories[END_REF][START_REF] Kroening | Decision Procedures: An Algorithmic Point of View[END_REF] for checking easier theories, but the development for quantifier-free non-linear real and integer arithmetic 14 is still in its infancy.

Figure 1 shows a non-exhaustive history of tool developments in these two areas. It illustrates nicely the historically deeper roots of computer algebra systems, but also the high intensity of research in both areas. The resulting tools are successfully applied in several academic and industrial areas, however, the current state is still not satisfactory, as described in [START_REF] Platzer | Real world verification[END_REF]: "Despite substantial advances in verification technology, complexity issues with classical decision procedures are still a major obstacle for formal verification of real-world applications, e.g., in automotive and avionic industries." Both communities address similar problems and share the challenge to improve their solutions to achieve applicability on complex large-scale applications. However, the Symbolic Computation community and the Satisfiability Checking community are largely in their own silos and traditionally do not interact much with each other.

To connect these communities, we successfully applied for a European Horizon 2020 Coordination and Support Action, with an envisaged project start in July 2016. The overall aim of this project is to create a new research community bridging the gap between Satisfiability Checking and Symbolic Computation, whose members will ultimately be well informed about both fields, and thus able to combine the knowledge and techniques of both fields to develop new research and to resolve problems (both academic and industrial) currently beyond the scope of either individual field. We call the new community SC 2 , as it will join the communities of Satisfiability Checking and Symbolic Computation.

The contributions of this paper are twofold: Firstly, we discuss the potentials of closer connection and more intensive exchange between the two communities, and list a number of challenges that are currently out of reach but could be tackled by a unified SC 2 community (Section 3). Secondly, we discuss what is needed to trigger and support these developments, and describe the actions of our project to satisfy these needs (Section 4).

Background

Before describing our project, we give a short description of the state-of-the-art in Satisfiability Checking and Symbolic Computation. Parts of this section are taken from [START_REF] Ábrahám | Building bridges between symbolic computation and satisfiability checking[END_REF].

Symbolic Computation and Computer Algebra Systems

Computer Algebra, the use of computers to do algebra rather than simply arithmetic, is almost as old as computing itself, with the first PhD theses [START_REF] Kahrimanian | Analytic Differentiation by a Digital Computer[END_REF][START_REF] Nolan | Analytic Differentiation on a Digital Computer[END_REF] dating back to 1953. This initial work consisted of programs to do one thing, but the focus soon moved on to 'systems', capable of doing a variety of tasks. One early such system was Collins' SAC [START_REF] Collins | The SAC-1 system: An introduction and survey[END_REF], written in Fortran. Many of the early systems were written in LISP, largely because of its support for recursion, garbage collection and large integers. The group at M.I.T. developed Macsyma [START_REF] Martin | The Macsyma system[END_REF] in the 1960s. about the same time, Hearn developed Reduce [START_REF] Hearn | REDUCE: The first forty years[END_REF], and shortly after a group at IBM Yorktown Heights produced SCRATCHPAD, then AXIOM [START_REF] Jenks | AXIOM: The Scientific Computation System[END_REF], a system that attempted to match the generality of Mathematics with some kind of generic programming, to allow algorithms to be programmed in the generality in which they are conventionally stated, e.g., polynomials over a ring.

Symbolic Computation was initially seen as part of Artificial Intelligence, with major triumphs such as [START_REF] Slagle | A Heuristic Program that Solves Symbolic Integration Problems in Freshman Calculus[END_REF] being "A Heuristic Program that Solves Symbolic Integration Problems in Freshman Calculus", firmly in the AI camp. By the end of the 1960s, this approach to integration had been replaced by an algorithm [START_REF] Moses | Symbolic Integration[END_REF], which had the great advantage that, when backed up with a suitable completeness theorem [START_REF] Risch | The problem of integration in finite terms[END_REF] it could prove unintegrability: "there is no formula made up of exponentials, logarithms and algebraic functions which differentiates to e -x 2 ", in other words "e -x 2 is unintegrable".

The 1960s and 70s also saw great advances in other areas. We had much more efficient algorithms to replace naive use of Euclid's algorithm for greatest common divisor computation (and hence the simplification of fractions), far better algorithms than the search-based methods for polynomial factorisation, and so on. All this meant that Symbolic Computation firmly moved into the camps of algorithmics and complexity theory, and the dominant question became "what is the worst-case complexity of this algorithm".

Gröbner bases. One great success of this period was the method of Gröbner bases [START_REF] Buchberger | Ein Algorithmus zum Auffinden des basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal[END_REF]. This allows effective, and in many cases efficient, solution of many problems of polynomials over algebraically-closed fields (typically the complex numbers, though applications over finite fields and in cryptography abound). This notion paved the way for the discovery of numerous effective methods for polynomial ideals; many applications in other areas of Mathematics quickly followed. Buchberger's algorithm for computing a Gröbner basis is a prime example of the huge gulf that can separate an abstract algorithm from a usably efficient implementation. Over the fifty years since its initial publication, research into the algorithm's behaviour has produced several significant improvements: the modern refined version is typically thousands of times faster than the original. The search for further improvements continues today.

The remarkable computational utility of Gröbner bases prompted the development of a number of distinct, independent implementations of refined versions of Buchberger's algorithm. The main commercial general-purpose computer algebra systems (including MAGMA [START_REF] Bosma | The Magma algebra system. I. The user language[END_REF], Maple [START_REF] Maple | [END_REF], Mathematica [58]) can all compute Gröbner bases; researchers needing the flexibility and ability to experiment with new algorithms also use computer algebra systems such as CoCoA/CoCoALib [START_REF] Abbott | CoCoA-5: A system for doing computations in commutative algebra[END_REF], Macaulay/Macaulay2 [START_REF] Grayson | Macaulay2, a software system for research in algebraic geometry[END_REF] and Singular [START_REF] Decker | Singular 4-0-2 -A computer algebra system for polynomial computations[END_REF] and Reduce [START_REF] Hearn | REDUCE: The first forty years[END_REF] which are freely downloadable from their respective websites.

Cylindrical algebraic decomposition. Another great success of the 1970s was the development of cylindrical algebraic decomposition (CAD) in [START_REF] Collins | Quantifier elimination for real closed fields by cylindrical algebraic decomposition[END_REF]. This replaced the non-elementary complexity (no finite tower of exponentials bounds the complexity) of Tarski's method for real algebraic geometry, by a doubly exponential method. A CAD is a decomposition of R n into cells arranged cylindrically (meaning their projections are equal or disjoint) and described by semi-algebraic sets. For a detailed description of modern CAD, see [START_REF] Bradford | Truth Table Invariant Cylindrical Algebraic Decomposition[END_REF].

Hong created a C version of both the SAC library and the comprehensive CAD code, which is now open-source and freely available as SACLIB and QEPCAD-B [START_REF] Brown | QEPCAD B: A program for computing with semi-algebraic sets using CADs[END_REF]. Another example is the Redlog package [START_REF] Dolzmann | Redlog: Computer algebra meets computer logic[END_REF] of the computer algebra system Reduce, which offers an optimised combination of the cylindrical algebraic decomposition with virtual substitution (see below) and Gröbner basis methods.

Virtual substitution. To mention a last algorithm, virtual substitution [START_REF] Weispfenning | Quantifier elimination for real algebra -The quadratic case and beyond[END_REF] focuses on non-linear real arithmetic formulas where the degree of the quantified variables is not too large. Although the method can be generalised to arbitrary degrees, current implementations are typically limited to input, where the total degree of the quantified variables does not exceed 2. In practice, this limitation is somewhat softened by employing powerful heuristics like systematic degree shifts or polynomial factorisation. One key idea is to eliminate existential quantifiers in favour of finite disjunctions plugging in test terms that are derived from the considered formula.

These methods and their numerous refinements belong to the usual tool box of state-of-the-art computer algebra systems, and enable them to tackle hard arithmetic problems.

Satisfiability Checking

In the 1960s, another line of research on Satisfiability Checking [START_REF] Biere | Handbook of Satisfiability[END_REF] for propositional logic started its career. The first idea used resolution for quantifier elimination [START_REF] Davis | A computing procedure for quantification theory[END_REF], and had serious problems with the steeply increasing requirements on computational and memory resources with the increase of the problem size. Another research line [START_REF] Davis | A machine program for theorem-proving[END_REF] suggested a combination of enumeration and Boolean constraint propagation (BCP). A major improvement was achieved in the 1990s by combining the two approaches, leading to conflict-driven clause-learning and non-chronological backtracking [START_REF] Marques-Silva | GRASP: A search algorithm for propositional satisfiability[END_REF]. Later on, this impressive progress was continued by novel efficient implementation techniques (e.g., sophisticated decision heuristics, two-watched-literal scheme, restarts, cache performance, etc.), resulting in numerous powerful SAT solvers.

Driven by this success, big efforts were made to enrich propositional SATsolving with solver modules for different existentially quantified theories. Highly interesting techniques were implemented in SAT-modulo-theories (SMT) solvers for checking, e.g., equality logic with uninterpreted functions, array theory, bitvector arithmetic and quantifier-free linear real and integer arithmetic, but the development for quantifier-free non-linear real and integer arithmetic is still in its infancy. For further reading, see, e.g., [START_REF] Barrett | Satisfiability modulo theories[END_REF][START_REF] Kroening | Decision Procedures: An Algorithmic Point of View[END_REF].

Modern SMT solvers typically combine a SAT solver with one or more theory solvers as illustrated in Figure 2. First the input formula is transformed into conjunctive normal form (CNF), a conjunction of disjunctions (clauses); this transformation can be done in linear time and space using Tseitin's transformation on the cost of additional variables. Next, the resulting CNF is abstracted to a pure Boolean propositional logic formula by replacing each theory constraint by a fresh Boolean proposition. Intuitively, the truth value of each fresh proposition defines whether the theory constraint, which it substitutes, holds. The SAT solver tries to find solutions for this propositional abstraction and during solving it consults the theory solver(s) to check the consistency of the theory constraints that should hold according to the current values of the abstraction variables.

On the one hand, theory solvers only need to check conjunctions (sets) of theory constraints, instead of arbitrary Boolean combinations. On the other hand, theory solvers should have the following properties for being SMT-compliant:

-They should work incrementally, i.e., after they determine the consistency of a constraint set, they should be able to take delivery of some additional constraints and re-check the extended set, thereby making use of results from the previous check. -In case of unsatisfiability, they should be able to return an explanation for inconsistency, e.g., by a preferably small inconsistent subset of the constraints. -They should support backtracking, i.e., the removal of previously added constraints.

Optimally, theory solvers should also be able to provide a satisfying solution, if the problem is satisfiable, and a proof of unsatisfiability for the explanation, if the problem is unsatisfiable.

A great advantage of the SMT technology is that it can employ decision procedures not only in isolation, but also in combination. For example, solving non-linear arithmetic formulas can often be speeded up by first checking linear abstractions or linear problem parts using more efficient decision procedures, before applying heavier procedures. Additionally, theories can also be combined already in the input language of SMT solvers. For example, deductive program verification techniques generate verification conditions, which might refer to arrays, bit-vectors as well as integers; in such cases, dedicated SMT solvers can apply several decision procedures for different theories in combination.

When combining decision procedures, incomplete but efficient procedures are also valuable, if they guarantee termination but not necessarily return a conclusive answer. Such incomplete methods are frequently applied in SMT solving, a typical example being interval constraint propagation, based on interval arithmetic. Some solvers combine such incomplete methods with complete decision procedures, in order to guarantee the solution of the problem, while increasing efficiency. Other solvers even sacrifice completeness and might return a "don't know" answer, but still they are able to solve certain extremely large problems, which are out of reach for complete methods, very fast. Furthermore, incomplete procedures are the only way to support problems from undecidable theories, like formulas containing exponential or trigonometric functions.

SAT and SMT solvers are tuned for efficiency. Combining complete and incomplete decision procedures, making use of efficient heuristics, learning not only propositional facts but also (Boolean abstractions of) theory lemmas at the SAT level allow modern SMT solvers to solve relevant large-size problems with tens of thousands of variables, which could not be solved before by single decision procedures in isolation. For some example applications see, e.g., [START_REF] Barrett | Problem solving for the 21st century: Efficient solvers for satisfiability modulo theories[END_REF].

Examples for solvers that are able to cope with linear arithmetic problems (either in a complete or in an incomplete manner) are Alt-Ergo [START_REF] Conchon | A collaborative framework for nonlinear integer arithmetic reasoning in Alt-Ergo[END_REF], CVC4 [START_REF] Barrett | CVC4[END_REF], iSAT3 [START_REF] Fränzle | Efficient solving of large non-linear arithmetic constraint systems with complex Boolean structure[END_REF][START_REF] Scheibler | Recent improvements in the SMT solver iSAT[END_REF], MathSAT [START_REF] Cimatti | The MathSAT5 smt solver[END_REF], OpenSMT2 [START_REF] Bruttomesso | The OpenSMT2 solver[END_REF], SMT-RAT [START_REF] Corzilius | SMT-RAT: An open source C++ toolbox for strategic and parallel SMT solving[END_REF], veriT [START_REF] Bouton | veriT: An open, trustable and efficient SMT-solver[END_REF], Yices2 [START_REF] Dutertre | A fast linear-arithmetic solver for DPLL(T)[END_REF], and Z3 [START_REF] De Moura | Z3: An efficient SMT solver[END_REF]. A further interesting SMT-approach for linear integer arithmetic is proposed in [START_REF] Bromberger | Linear integer arithmetic revisited[END_REF].

Much less activity can be observed for SMT solvers for non-linear arithmetic. A few SMT tools embedded some (complete as well as incomplete) decision procedures. Such a solver is iSAT3, which uses interval constraint propagation. The SMT solver MiniSmt [START_REF] Zankl | Satisfiability of non-linear (ir)rational arithmetic[END_REF] tries to reduce non-linear real arithmetic problems to linear real arithmetic and can solve only satisfiable instances this way. We are aware of only two SMT solvers that are complete for non-linear real arithmetic: Firstly, the prominent Z3 solver developed at Microsoft Research, which uses an elegant SMT-adaptation of the cylindrical algebraic decomposition method [START_REF] Jovanović | Solving non-linear arithmetic[END_REF]. Secondly, SMT-RAT [START_REF] Corzilius | SMT-RAT: An open source C++ toolbox for strategic and parallel SMT solving[END_REF], using solver modules for simplex, the cylindrical algebraic decomposition, the virtual substitution method, Gröbner bases, interval constraint propagation, branch and bound, and their strategic combination [START_REF] De Moura | The strategy challenge in SMT solving[END_REF].

Even fewer SMT solvers are available for non-linear integer arithmetic, which is undecidable in general. A linearisation approach was proposed in [START_REF] Borralleras | Solving non-linear polynomial arithmetic via SAT modulo linear arithmetic[END_REF]. The SMT solving spin-off of AProVE [START_REF] Codish | Exotic semi-ring constraints[END_REF] uses bit-blasting. To our knowledge, Z3 implements a combination of linearisation and bit-blasting. iSAT3 uses interval constraint propagation, whereas Alt-Ergo combines the idea of [START_REF] Bobot | A simplex-based extension of Fourier-Motzkin for solving linear integer arithmetic[END_REF] with an axiom-based version of interval constraint propagation. SMT-RAT can tackle this theory using a generalised branch-and-bound technique.

The increasing variety of the theories considered by SMT solvers created an urgent need for a common input language. The SMT-LIB initiative [START_REF] Barrett | The satisfiability modulo theories library (SMT-LIB )[END_REF] defined a standard input language for SMT solvers with a first release in 2004, and provides a large and still increasing number of benchmarks, systematically collected for all supported theories. SMT-LIB also enabled the start of SMT competitions; the first one took place in 2005 with 12 participating solvers in 7 divisions (theories, theory combinations, or fragments thereof) on 1360 benchmarks, which increased in 2014 to 20 solvers competing in 32 divisions on 67426 benchmarks. The SMT-LIB standard and the competitions not only intensified the SMT research activities, but also gave visibility and acceptance for SMT solving in computer science and beyond. Once a problem is formulated in the SMT-LIB language, the user can employ any SMT solver to solve the problem.

Some Scientific Challenges and Opportunities

On the one hand, SMT solving has its strength in efficient techniques for exploring Boolean structures, learning, combining solving techniques, and developing dedicated heuristics, but its current focus lies on easier theories and it makes use of Symbolic Computation results only in a rather naive way. There are fast SMT solvers available for the satisfiability checking of linear real and integer arithmetic problems, but just a few can handle non-linear arithmetic. On the other hand, Symbolic Computation is strong in providing powerful procedures for sets (conjunctions) of arithmetic constraints, but it does not exploit the achievements in SMT solving for efficiently handling logical fragments, using heuristics and learning to speed-up the search for satisfying solutions.

The Satisfiability Checking community would definitely profit from further exploiting Symbolic Computation achievements and adapting and extending them to comply with the requirements on embedding in the SMT context. However, it is a highly challenging task, as it requires a deep understanding of complex mathematical problems, whose embedding in SMT solving is not trivial.

Symmetrically, Symbolic Computation could profit from exploiting successful SMT ideas, but it requires expertise in efficient solver technologies and their implementation, like dedicated data structures, sophisticated heuristics, effective learning techniques, and approaches for incrementality and explanation generation in theory solving modules.

In this section we describe some ideas of how algorithms and tools from both communities could be made more powerful by exploiting scientific exchange and technology transfer.

Symbolic Computation Techniques for Satisfiability Checking

Many practical decision procedures, designed by the Symbolic Computation community, are implemented in computer algebra systems (e.g., linear real and integer arithmetic, non-linear real arithmetic, linear programming, quantified formulas, Gröbner and involutive bases). To use them in a Satisfiability Checking context, some scientific and engineering issues need solutions, notably to find new ways of incremental solving, explaining unsatisfiability and generating lemmas.

Whereas for linear real arithmetic useful procedures have been adapted to satisfy the requirements for SMT embedding, many opportunities remain to be explored for non-linear arithmetic. For example, there are (to the best of our knowledge) just two SMT solvers, Z3 and SMT-RAT, which make use of the CAD method, but in a different way: Z3 uses a very elegant solution to explore the state space by a close integration of theory decisions and theory propagation in the Boolean SAT search, and constructs CAD only partially to explain conflicts in the above search (more precisely, to compute a semi-algebraic description of CAD cells that do not satisfy a given sign condition). In contrast, SMT-RAT implements an incremental version of the CAD method, which works hand-in-hand with the search at the logical level. For this latter approach, the power of heuristics (variable and polynomial ordering for incremental projection, choice and order of sample points for lifting) and the generation of lemmas (most importantly the computation of explanations for unsatisfiability) is still far from being fully exploited.

There is still great potential for improvements not only for the SMT embedding of the CAD method, but also other non-linear arithmetic decision procedures like virtual substitution or Gröbner bases, and their strategic combination with each other and further light-weight methods such as interval constraint propagation.

Another important aspect is the Symbolic Computation community's expertise in simplification and preprocessing. The complexity of the problems this community handles is often extremely high, and no practical procedure would exist without significant techniques to prepare the input problems. Such techniques do exist for Satisfiability Checking, but they rather focus on easier theories. A transfer of the savoir-faire in simplification and preprocessing for non-linear real and integer arithmetic would certainly be highly profitable.

Satisfiability Checking Techniques for Symbolic Computation

A key ingredient in the success of the Satisfiability Checking tools is the use of learning and non-chronological backtracking techniques to speed up the search through tree-shaped search structures. Traditionally (and in the majority of cases) CAD proceeds through a two stage process: first, projecting the problem through lower dimensions; then lifting: incrementally building a solution in increasing dimensions. An alternative approach using triangular decomposition was introduced in [START_REF] Chen | Computing cylindrical algebraic decomposition via triangular decomposition[END_REF] where first the complex domain is cylindrically decomposed and then refined to a CAD of the real domain, where all data is in a tree-shaped structure.

Other techniques are certainly amenable for learning with the non-chronological backtracking approach. For instance, first prototypes integrating CDCL-style learning techniques with virtual substitution for linear quantifier elimination have been successfully created and studied. Integration of learning techniques with the computation of comprehensive Gröbner bases [START_REF] Weispfenning | Comprehensive Gröbner bases[END_REF] should also be investigated.

Incrementality, which played an important role in the success of Satisfiability Checking, may also be used to make Symbolic Computation techniques more efficient. The alternative CAD construction method described above is also incremental in nature [START_REF] Bradford | Truth table invariant cylindrical algebraic decomposition by regular chains[END_REF] and so may offer one option here. An incremental CAD-based decision procedure for solving polymial constraint systems was proposed in [START_REF] Strzeboński | Solving polynomial systems over semialgebraic sets represented by cylindrical algebraic formulas[END_REF]. There exist algorithms for Gröbner bases which exploit known mathematical facts about the ideal generated by the basis like its Hilbert function or some syzygies. Traditionally, this has been seen as a way to speed up computations. However, these approaches can naturally be adapted into incremental algorithms.

A central aspect of Satisfiability Modulo Theories is the combination frameworks for theories and decision procedures. Combining theories in Symbolic Computation (combined real/floating point theories, interval constraint propagation with other arithmetic theories) might also bring a number of advantages and possibilities, for instance, more expressive languages, or efficiency due to hierarchical reasoning. While combination of theories in Symbolic Computation are typically very specific and ad hoc, the SMT community systematically uses the generic Nelson-Oppen framework [START_REF] Nelson | Simplifications by cooperating decision procedures[END_REF] for disjoint theories. Such a framework can of course not be used as it is, but it might be an inspiration for a modular approach in Symbolic Computation.

Standard Languages and Benchmarks

The initiation and maintenance of a common problem specification language standard SMT-LIB [START_REF] Barrett | The satisfiability modulo theories library (SMT-LIB )[END_REF] and of competitions form an important part of the Satisfiability Checking community effort. Besides providing a stimulating event for tool developers to exhibit their systems, the competitions are also a vehicle for publishing practical progress. Competition results are advertised, and consulted by users to pick the best tools and techniques to solve problems.

The Symbolic Computation community does not have a similar tradition, and indeed, to quote one major system developer: "it is very hard to get any practical improvements published -the reviewers will often say this is not hard science". Although it is not good to only focus on a small library of benchmarks and have the competition as sole goal, competitions do have a tremendously positive effect on tools and techniques, as witnessed in the Satisfiability Checking community, especially if the competition challenges are concrete industrial challenges. Such driving forces could be also established in Symbolic Computation.

Though in Satisfiability Checking the standard input language allowed to provide large benchmark sets to the community, benchmarks for non-linear arithmetic theories are still rare, and harder to describe without ambiguity. Therefore, also the Satisfiability Checking community would profit from a common standard with an increased number of non-linear arithmetic benchmarks.

The solution of challenging problems, as mentioned in the previous section, could be within reach, when supported by a stronger collaboration between both SC 2 research areas, creating an infrastructure for dialogue and knowledge transfer. However, the research areas of Satisfiability Checking and Symbolic Computation are still quite disconnected, as reflected in their communication platforms and support structures. Symbolic Computation has its own conferences (ACA, CASC, ISSAC, etc.), several dedicated journals (e.g., AAECC, JSC, MSC), and the SIGSAM forum. Similarly, Satisfiability Checking is supported by its own conferences (CADE, IJCAR, SMT, etc.) and journals (e.g., JAR), the SatLive forum to keep up-to-date with research, SMT standards, and SAT-and SMTsolver competitions.

The main aims of our project are to create communication platforms and propose standards to enable the interaction between the two communities, and to use these platforms to initiate discussions and cooperation and to identify potentials, challenges and obstacles for future research and practical applications. In the following we shortly describe planned actions of our SC 2 project to achieve these goals.

Communication platforms To bridge the SC 2 communities, we will initiate platforms to support the interaction of the currently disjoint groups. We organised a Dagstuhl Seminar Symbolic Computation and Satisfiability Checking 15 15-20th November, 2015, which already led to numerous interesting discussions and interactions. At CASC 2016, we will organise a topical session devoted to topics from the cross-community SC 2 area. Furthermore, we will establish a workshop series in the area of SC 2 , covering the interests of both communities, and having its first edition affiliated with SYNASC 2016. These workshops will serve as platforms for scientific exchange, discussion and cooperation within and between the currently disjoint communities. To support and attract young new community members, we will organise a dedicated summer school aimed at interested young researchers from SC 2 areas, with courses specifically tailored to their needs.

Research roadmap

The above platforms will initiate cross-community interactions, and help to clearly identify unused potentials. We aim at initiating discussions on what the communities can learn from each other, what are the common challenges which they can solve together, what Satisfiability Checking could learn from Symbolic Computation achievements, and which Satisfiability Checking results could be adapted to improve Symbolic Computation solutions.

Our long-term objective is to create a research roadmap of potentials and challenges, both to the two traditional subject silos, but also challenges that only the new joined SC 2 community can address. This roadmap should identify, within the problems currently faced in the industry, the particular points that can be expected to be solved by the SC 2 community in the short and middle term, and will provide recommendations for spin-off projects.

Standards, benchmarks, competitions We aim to create a standard problem specification language capable of representing common problems of the SC 2 community. We plan on extending the SMT-LIB language, which is already mature and fully accepted among the SMT (Satisfiability Checking) community, to handle features needed for the Symbolic Computation community. This will be done in a modular way, with a particular focus on extensibility for new features.

Agreeing on a common language, and being able to share challenging problems is an essential aspect for building a dynamic community. This will foster further discussions and uncover problems that can be solved by the SC 2 community altogether, set clear challenges on which various approaches can be evaluated, classify the approaches according to their strength and weaknesses on the various kinds of problems. Mixed approaches will naturally emerge, to tackle problems exhibiting several orthogonal difficulties. The standard could also serve as a communication protocol for platforms mixing tools, to build meta-tools to solve large and difficult problems out of reach of current techniques often specialised to just one kind of job.

How to become an associate? This project cannot reach its aims by involving just a small number of core project members. To be able to cover sufficiently wide research and application areas and to take into account their needs and interests, there are currently 37 SC 2 associates from both research communities as well as from industry. Our associates will be regularly informed about the project activities and they will be invited to take part in the corresponding events.

The SC 2 Coordination and Support Action will be an optimal platform for industrial and academic partners and associates to form smaller working groups and initiate specific projects. If you would like to participate in the project as an associate, please contact the Project Coordinator James Davenport 16 .

Conclusions and Future Work

In this paper we gave a short description of the aims and actions of our upcoming EU Coordination and Support Action SC 2 .

The SC 2 project will maintain a website (http://www.sc-square.org) making readily accessible all the public information of the project (e.g., contact information, details of past and forthcoming SC 2 workshops and other similar events).

Fig. 1 .

 1 Fig.1. History of some computer algebra systems and SAT/SMT solvers (not exhaustive; years approximate first release as far as known and as positioning allowed)[START_REF] Ábrahám | Building bridges between symbolic computation and satisfiability checking[END_REF]

Fig. 2 .

 2 Fig. 2. The functioning of SMT solvers

It is usual in the SMT community to refer to these constraints as arithmetic. But, as they involve quantities as yet unknown, manipulating them is algebra. Hence both words occur, with essentially the same meaning, throughout this document.

Acknowledgements

We thank the anonymous reviewers for their comments. We are grateful for support by the H2020-FETOPEN-2016-2017-CSA project SC 2 (712689) and the ANR project ANR-13-IS02-0001-01 SMArT. Earlier work in this area was also supported by the EPSRC grant EP/J003247/1.