Sebastien Postic
email: sebastien.postic@mines-paristech.fr

Sandrine Selosse

Nadia Maïzi

Energy sector contribution to regional climate action: The case of Latin America

The most optimistic Representative Concentration Pathway (RCP 2.6) in the fifth IPCC Assessment Report predicts a 0.3°C to 1.7°C global mean temperature change in 2100, putting natural species and systems at risk, possibly triggering large-scale irreversible natural damage, and strongly impacting human activities (IPCC, 2014). In South America and the Caribbean, a region representing a relevant share of global GHG emissions with a weight of 7.7% in 2011 (World Resources Institute, 2015), slightly more than its share of the world's population (6.9% in 2010), the latest estimates point to a 1.5% to 5% GDP loss by 2050 [START_REF] Samaniego | The economics of climate change in Latin America and the Caribbean: Paradoxes and challenges[END_REF]. Particularly, Brazil already ranks fourth in the world when it comes to national contributions to global warming (Matthews et al., 2014) and a strong increase in GHG emissions can be anticipated in the years to come throughout the region on a BAU basis (Carvallo et al., 2014;Fundación Bariloche, 2008;[START_REF] Van Ruijven | Baseline projections for Latin America: baseyear assumptions, key drivers and greenhouse emissions[END_REF]. In this context, quite logically, the region has a relevant role to play in mitigating global emissions. No South American countries are included in Annex I of the United Nations Framework Convention on Climate Change (UNFCCC) and as such, before the Paris Agreement on climate change signed in December 2015 in Paris during the COP 21, they were not bound to any GHG quantified emission reduction. They had, however, been invited to voluntarily commit to Nationally Appropriate Mitigation Actions (NAMAs). Part of the Copenhagen Accord, NAMAs provide a flexible framework within which non-Annex I countries can pledge voluntary actions at an economy-wide or sectorial level, aimed at deviating from BAU emissions [START_REF] Sharma | Understanding NAMA Cycle[END_REF]. The nature, quantification and implementation roadmap 1 of these NAMAs vary considerably across South America.

Chile has pledged emission reductions of 20% by • 2020, compared to a 2009 Business-As-Usual scenario (BAU); there is no quantified measure in its engagement letter concerning how this target will be met, and little description. Energy efficiency, renewable energies and AFOLU (Agriculture, Forestry and Other Land-Use) are specified as the main action sectors for these reductions.

Brazil has based most of its pledge on quantified • emission reductions in the field of deforestation and more generally the AFOLU sector. These sectorial reductions have been aggregated into an estimated national target of 36.6% to 38.9% emission reductions below a national baseline by 2020.

Colombia has committed to 77% renewables in its • installed electricity production capacity by 2020, and 20% biofuels in overall fuel consumption.

Peru has pledged a 0% net deforestation rate by • 2021, as well as a minimum of 33% renewable energy in all energy consumed in the country, and nonquantified measures for waste emissions reduction. The country has not quantified the overall impact of these pledges, but independent academics estimate that the measures should lead to a 41% GHG reduction compared to BAU (Hof et al., 2013).

With the exception of small countries such as Antigua and Barbuda, the rest of the continent has so far made no pledges to the UNFCCC. However, national communications emphasize national measures and strategies in:

Argentina: energy efficiency programs, renewable energy including biofuels and hydrogen, forest management, • solid waste management; Ecuador: by 2020, • 82% of oil in primary energy, down from 92% in 2011 At least 90% renewable electricity, 80% from hydropower Uruguay: the National Plan to 2015 aims at over 15% electricity from unconventional renewable sources • Paraguay: the country has set reforestation targets and expressed its intention to expand energy-crop cultures. • This list is far from exhaustive for national targets and measures that are not bound to the UNFCCC.

The energy sector, the largest contributor to GHG emission, shows promising potential to achieve climate mitigation worldwide (Akimoto et al., 2010) and South American NAMAs consider it extensively. However, the potential of the South American energy sector may remain below world averages (Bassi and Baer, 2009;Borba et al., 2012;Di Sbroiavacca et al., 2015), because of an already-renewable energy mix, fast energy growth -the electrification rate jumped from 75% in 2009 to around 90% in 2012 in Peru and Bolivia (CIER, 2013(CIER, , 2011) ) -and the use of energy as a tool for domestic and international policy (Colgan, 2014).

Given Latin America's regional specificities, what contributions can its energy sector make to the fight against climate change, and at what cost? This paper investigates this specific aspect of the energy-climate nexus in Latin America through the prism of ongoing climate negotiations. This analysis focuses on the climate commitment of Latin America pledged before the Intended Nationally Determined Contributions (INDCs) asked to publish through the 2015 United Nations Climate Change Conference held in Paris in December and which led to the signing of a historical global agreement on climate change. We use a bottom-up energy prospective model from the MarkAl/TIMES family with four contrasted scenarios for future climate policies in South America, presented in section 2. In section 3, we study the energy sector's contribution to meeting regional climate pledges and the evolutions that such a contribution implies. We start by considering the specific case of the power mix then expand our study to the whole total primary energy supply, underlining the role of Brazil and Chile in driving the energy transition in South America. We also consider the efficiency and impact of Peru and Colombia's national commitments and the links between the AFOLU sector, the energy sector and the fight against climate change in Latin America.

The results presented and discussed in this paper are based on the T-ALyC model. T-ALyC, standing for TIMES para América Latina y el Caribe, (TIMES for Latin America and the Caribbean), is a multiregional model based on the TIMES paradigm for long-term energy prospective. This modeling approach developed under IEA's Energy Technology Systems Analysis Program (IEA-ETSAP) Agreement considers a bottom-up representation of the energy system and relies on linear optimization techniques to meet an exogenous energy service demand at the lowest possible discounted cost, over a given time horizon (typically 2010-2050). The energy system is explicitly represented through a few thousand energy processes and commodities and their individual features (efficiency, investment costs, O&M costs, emission factors, etc.). Demand satisfaction is subject to resource constraints (resource availability, extraction cost), technical constraints (physical balances, availability factors, process lifetimes, etc.) and non-technical constraints (market penetration limits, policy scenarios, environmental specifications, etc.). For more information on the TIMES paradigm and its implementation, please refer to (Loulou et al., 2005). TIMES models minimize the cost of delivering a given energy service through both investment in, and operation of, energy processes. The outputs of TIMES models are the evolution and final structure of the energy system, individual investment and operation costs for each modeled technology, process-related and fuel-related emissions, energy trade flows between model regions and with the rest of the world, and the marginal cost of political constraints such as emission pledges.

II -Methods and scenarios

2-1 -The T-ALyC model

www.cma.fr Energy sector contribution to regional climate action: the case of latin America T-ALyC's technological description is inherited from the TIMES Integrated Assessment Model TIAM, a 15-region representation of the whole world's energy system, from resource extraction to end-use energy demands (Loulou and Labriet, 2008;Ricci and Selosse, 2013;[START_REF] Syri | Global energy and emissions scenarios for effective climate change mitigation-Deterministic and stochastic scenarios with the TIAM model[END_REF]. The Reference Energy System is split into a module for fossil fuel extraction, a transformation module from primary to refined fuels (including biomass transformation), an energy conversion module for electricity and heat production, and 5 end-use demand sectors, as shown in Figure 1. T-ALyC considers the entire Latin America and the Caribbean region, excluding Mexico (conforming with the current Central and South America region in TIAM). T-ALyC relies on an ad hoc disaggregation of the area into 10 sub-regions (cf. Table 1) to address region-specific issues including the role of hydropower and interrogations about its future development, the current and future role of biofuels in the energy mix, challenges, opportunities and time dynamics of regional integration and the climate change-energy nexus. T-ALyC thus emphasizes in its geographical structure the main geo-energy trends of the continent, which include among others the weight and diversity of Brazil, the strategic interconnecting role of Bolivia, Paraguay, Uruguay and Central America, and the diverging paths of Chile and Argentina. The base year for model projections is 2010 and the end horizon is 2050. This time span is divided into 6 time periods, then 6 representative time slices in each period (three seasons: Winter, Summer, Intermediate; two diurnal divisions: Day, Night).

Region name

2-2 -Climate scenarios

We investigate the impact of climate negotiations on the South American energy sector through 4 scenarios, namely "Business-As-Usual" (BAU), "Brazil and Chile only" (BraChi), "All Nationally Adapted Mitigation Actions" (NAMAs) and "Quantified reductions for all" (Red4All).

The Business-As-Usual scenario considers that no climate pledge is taken by any country. It allows us to present the key energy determinants of the continent, and serves as a comparison point for our climate pledge scenarios. We also use it to set the targets for climate scenarios, when such targets are defined as a reduction below a national emission baseline.

Brazil and Chile only is the least stringent climate scenario, considering only quantified reduction pledges for Brazil and Chile. For Brazil, our target is less stringent than that pledged in 2010, since the original objective was based on national BAU projections. We did not have access to this BAU, but the fight against deforestation improved dramatically between 2005 and 2010, so we can assume that part of the objective has already been met (emissions in 2010 and after in our own BAU are calibrated based on updated national inventories and are already much lower than in 2005). Also, Brazil's constraint is written as an overall cap for the joint emissions of the two-region Brazil, meaning that the choice of where to reduce emissions is left to the model. Both Brazil and Chile's targets are extrapolated to a 40% reduction below BAU in 2050.

All Nationally Adapted Mitigation Actions considers that UNFCCC pledges as described in the Introduction are implemented in Brazil, Chile, Colombia and Peru, plus a 30% deforestation reduction in Ecuador. Unlike for Brazil and Chile, the pledges for Colombia, Peru and Ecuador do not become stronger between 2020 and 2050. National voluntary policies that have not led to an NAMA pledge to the UNFCCC were not included in our modeling hypotheses.

Last, in Quantified Reductions for all, we consider that all countries make Chilean-like pledges on their future emissions. The only exceptions are Venezuela, Suriname, and Guyana. We consider that Venezuela would not adhere to any international agreements on climate3 and the data we have on Suriname and Guyana is too poor to make any valuable projection concerning climate commitments. These assumptions are summarized in Table 4. --

Region

- -20% - - - - - - - - - - - - - - - - - - - -20% - - - -20% - -25% -25% -25% - -25% -25% -25% - -20% -20% -20% - -40% -40% -40% - -40% -40% -40% - -40% -40% -40% - - NAMAs -20% - - NAMAs -40% - - - -40% - - - -40%
--

NAMAs -40%

--

--40%

Table 4: Scenario assumptions for regional emission targets www.cma.fr

Energy sector contribution to regional climate action: the case of latin America In the following paragraphs we detail this first insight, by comparing our Business-As-Usual projections with climate scenarios at sub-region and sector level. We first consider the power mix, then total primary energy production.

III -Results and discussion: Impact of climate pledges on the Energy sector

3-1 Impact of climate pledges on electricity

In 2012, South America already boasted a highly renewable electricity mix, with more than 60% of hydro-sourced electricity (CIER, 2013). The remaining electricity production was mainly made up of fossil fuels (gas, oil and coal) and nuclear power, leaving some room for improvement. Electricity generation is bound to almost double between 2010 and 2050, reflecting the region's forecasted strong growth, and this could, in principle, increase the share of carbon-emitting electricity sources in the energy mix, under BAU conditions. Figure 4, however, shows a completely different outcome in our projections. Despite a 92% increase in electricity generation, the share of fossil fuels drops sharply between 2012 and 2040. Similarly, while hydro production keeps increasing in absolute terms -from 677 TWh in 2010 to 1554 TWh in 2050, its share stabilizes in 2030, then starts dropping in the last two decades. The production gap is filled mainly by wind-and solarbased electricity production. The implications of such a result are already highly interesting: with no other assumption apart from cost minimization on a long-term horizon, the model already chooses green energies as the most interesting options for electricity production. This is partly due to the fact that this scenario occurs in an ideal world where long-term centralized planning is the rule. In practice, authors such as (Arango and Larsen, 2010) have stressed the fact that market forces and national policies in e.g. Argentina may lead to a carbonization of the electricity matrix in the years to come. However, our results imply that moving from a nearly 100% renewable power mix today to a 100% renewable mix tomorrow in South America is more about social acceptation and economic limitation than its lack of technical or economic potential.

Figure 5 displays the variations in power generation for our three climate scenarios compared to BAU, from the least stringent (BraChi) to the most stringent (Red4All). The impact of climate pledges on the energy sector appears clearly: the reliance on fossil fuels decreases in the three climate scenarios, and more so as time goes by. The amount of electricity generated under emission constraints is also slightly higher than in our BAU case, and so are electricity prices. Energy sector contribution to regional climate action: the case of latin America

We can detail this 'razor edge' effect for Colombia, in the NAMAs scenario. As a reminder, sectorial NAMAs were only proposed by Peru/Ecuador and Colombia (T-ALyC's AND and COL regions). They lead to an additional emissions reduction of 380 Mt CO2eq in 2050 on the continent compared to BraChi, which is a further 6.2% below BAU. Figure 6 presents the evolution of the power mix, from BraChi to NAMAs, in three cost scenarios:

The first one (NAMAs in the key on the figure) is the BAU cost scenario.

•

In NAMAs_1%, both the investment and O&M costs for mid-price dam technology increase by 1%, to 1.290 $/W • and 2.42 cts/W/yr, respectively. In NAMAs_2%, both the investment and O&M costs for mid-price dam technology increase by 2%, to 1.300 $/W • and 2.44 cts/W/yr, respectively.

While this cost evolution does not impact the power mix in the AND region, the effect is quite disproportionate for COL: in the regular NAMAs scenario, most decentralized PV generation is displaced by hydropower, but this effect disappears completely with 2% higher dam costs. The cost structure is different for decentralized PV and centralized hydro production: in the decentralized PV case, investment costs are high and daily availability is constrained, but we consider no operation and maintenance costs, no transmission costs and/or losses. Investment costs are lower for hydropower, yet this technology is burdened by fixed operation and maintenance costs, transmission costs and transmission losses. However, the present value of the electricity generated by these two technologies in 2050 differs very little. Climate constraints increase the volumes and marginal costs of electricity production and favor the latter, as a consequence of the aforementioned 'razor edge' effect. In AND, NAMAs induce an increase in wind, solar and hydro energy in the electricity mix, while biomass is redirected towards heat production. However, the added impact of the NAMAs scenario on the electricity mix is rather limited. This is mainly due to two factors: first, the only regions where NAMAs apply, namely AND and COL, together represent 11% of the electricity generated in South America in 2010 (15% in 2050). Second, unlike Chile and Brazil's pledges, which are based on BAU projections, the electricity targets registered as NAMAs for COL and AND are already partially met under BAU conditions.

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3-2 -Impact of climate pledges on primary energy consumption 3-2-1-The relevance of oil exports

When taking export-bound oil production into account, fossil fuels dominate primary energy production, constantly accounting for more than 70% of total production (Figure 7). In 2030, fossil fuels represent 80% of Latin American primary production; oil alone makes up 60% of this production, at 1,186 Mtoe.

The decrease in oil production after 2030 is owed to two factors (see Figure 8). The conjunction of those factors starts a downward trend for oil production in 2030. In the 2030-2050 period however, the rise of biomass and solar energy in the primary mix offsets this trend, leading to nearly stationary primary energy consumption between 2030 and 2050. However, primary solar energy as considered here is the incoming solar radiation before conversion into electricity 4 . As a consequence, the contribution of both biomass and solar energy to primary energy consumption is significantly larger than their actual output in terms of electricity/fuel/heat production.

4 That is, without the energy losses incurred by solar panels/connecting lines. About 85% of this primary energy is lost in the conversion process. Energy sector contribution to regional climate action: the case of latin America

The overwhelming majority of exported oil is crude, with few associated emissions. Nevertheless, climate pledges could still impact oil trade in South America, in three main ways: Regardless of decisions and pledges from other world regions, penalizing the regional consumption of fossil fuels (through taxes, subsidies on green fuels, etc.) would indeed make them less competitive on the internal market, but would not impact exports' competitiveness. We can thus expect that the decrease in primary fossil energy production will at best be limited, with a shift from internal consumption to exports. Financing a green subsidy policy could even lead to an increase in oil production when the takeoff of renewables is bound to the redistribution of an oil rent, as studied by (Goldemberg et al., 2014). Export volumes can be voluntarily reduced as part of a political volition to reduce the continent's contribution to global emissions. The Yasuni-ITT initiative, although unsuccessful, established an interesting case for this type of new cooperation framework (Pellegrini et al., 2014;[START_REF] Vallejo | Leaving oil underground in Ecuador: The Yasuní-ITT initiative from a multi-criteria perspective[END_REF]. Export volumes can also drop as a result of international climate pledges, through their impact on global oil prices. The idea here is that international pledges would push renewable energy production and reduce global oil demand, thus bringing down oil prices. Venezuela produces heavy oil at relatively high costs (breakeven price estimated at USD 30, compared to USD 10 for Saudi Arabian wells) and would be among the first impacted by such a slowdown (its budget breakeven is considered by most analyses to be around or above USD 120). This assumption is confirmed by studies such as e.g. [START_REF] Van Ruijven | Baseline projections for Latin America: baseyear assumptions, key drivers and greenhouse emissions[END_REF]. Another route could be a global border tax system, which would place oil exports on a level field with internal oil consumption (see e.g. (Keen and Kotsogiannis, 2014)) but have a detrimental effect on national industries. The risk inherent to such a scenario would be that the no-longer-exported oil could be consumed within Latin America itself, replacing other renewable forms of energy production, starting with biofuels. As a first approximation of this issue, Figure 9 presents the evolution of the primary energy mix (net of trade) in a global context with oil prices 40% lower than their BAU value: solar energy all but disappears from the energy mix, and some gas is also replaced.

3-2-2-Brazilian pledges drive regional decarbonization

Figure 10 shows primary energy production in Latin America minus net energy trade. The total primary energy supply is multiplied by slightly more than 2.5 between 2010 and 2050. The share of oil is considerably reduced (from 60% down to 35% in 2030) and, conversely, the share of gas increases, mainly due to net gas imports from Brazil and Chile. The overall fossil fuel share remains below 70% of total primary consumption during the whole period, yet the mix is quite heavily fossil-fuel based. While the power sector is the first fossil fuel consumer in 2010, the demand for fossil fuels is increasingly driven by industry and transport (Figure 11), as electricity depends less and less on fossil fuels5 .

Beyond relatively virtuous power production, BAU projections for energy production in Latin America thus leave some room for GHG emission reductions, most of all in the transport and industry sectors. This decarbonization potential could be tapped through biofuel policies, energy efficiency measures, investment in clean generation and transportation, modal shift, etc. We consider here the impact of pledge reductions as is, that is, without choosing a particular sector to achieve emission reductions ex ante, and without implementing any other ad hoc scheme than those described in Introduction. Energy sector contribution to regional climate action: the case of latin America Figure 12 displays the variations in primary energy supply (net of trade) for the three climate scenarios compared to BAU, from the least stringent (BraChi) to the most stringent (Red4All). As for electricity, the decline in fossil fuels is noteworthy; a new element, however, is the higher penetration of natural gas in primary energy. Under climate constraints, the industry sector shifts from coal to gas for steam and process heat generation, most of all in the two Brazil regions (BSE and BWC). BSE's industrial sector still exhibits a strong reliance on biomass (bagasse) in the three scenarios. Transport shifts heavily from oil-based fuels to biodiesel, with more than 40 Mtoe/yr new bio-based fuels in 2050 in the Red4All scenario. Both gasoline and diesel are impacted by this trend. All in all, a little more than 15% of the continent's 2050 primary energy production is transferred towards greener energy sources in the most stringent climate scenario, Red4All.

We now compare the BraChi scenario, where only Brazil and Chile's pledges are considered, with our BAU scenario. Figure 13 shows the impact of Brazil and Chile's pledges on energy trade in South America. BraChi pledges result not only in a decrease in national fossil fuel production and an increase in renewablebased energy production for the countries concerned; they also impact the rest of the continent through trade. BPU oil exports to Brazil and AND exports to Chile drop due to oil's reduced competitiveness in these two countries.

Bolivia increases its gas exports to Brazil until 2040; however, this increase exhausts Bolivian low-cost gas reserves, leading Brazil to shift to global markets to import its oil in the last period (2050). Finally, and most importantly, Colombia slows down its coal exports to Brazil (and, to a lesser extent, Chile), preferring to export its coal out of South America. This impact is far from negligible, as the coal redirected towards global markets in 2040 and 2050 represents more than 70% of total Colombian coal exports to Brazil -which, in turn, represent nearly all of Brazil's coal consumption in 2050. Brazilian pledges to reduce emissions below BAU make fossil fuels less competitive in the country, and Brazil's economic weight6 also drives their reduced competitiveness in neighboring countries, which translates into lower fossil fuel consumption inside South America itself and more exports outside the subcontinent.

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3-2-3-Sectorial targets: limited impact on energy

Let us now move to the NAMAs scenario. As already stated in paragraph 3.1, sectorial NAMAs have only been proposed by Peru/Ecuador and Colombia (T-ALyC's AND and COL regions). They lead to an additional emissions reduction of 380 Mt CO2eq in 2050 on the continent compared to BraChi, which is an additional 6.2% below BAU. However, this emissions reduction burden is not shared equally: for AND, emission reductions in 2050 under NAMAs assumptions represent 35.1% of all BAU emissions, while they account for 3.2% of BAU emissions in COL. There are two explanations for this difference: First, Colombia's primary energy consumption is much less impacted by national NAMAs than Peru's (Figure 14). In the Andean region, bio-based energy production increases by up to 26.9 Mtoe/yr in 2050 compared to the BraChi scenario, that is, the increase represents 23% of AND total primary energy production in 2050 in BraChi7 . On the other hand, primary energy production is only slightly impacted in 2050 in Colombia: the lower reliance on fossil fuels in 2050 (-3.03 Mtoe/yr) represents only a 2.8% deviation from Colombia's primary energy mix in BraChi. The main reason is that Colombia's NAMAs are already satisfied in our BAU projections, and more so in the BraChi scenario. This highlights one drawback of NAMAs compared to pledges for global reductions below a Business-as-Usual projection: while the latter always forces a change in the trend, the former may only follow the trend, with little if any impact. Second, Peru and Ecuador's NAMAs include a strong commitment to reduce deforestation, while Colombia's national objectives in this area are not formalized as UNFCCC pledges. Beyond real but limited improvements through the energy mix, deforestation pledges account for 332 MtCO2eq avoided emissions in the AND region; in other words, 90% of AND's emission reductions result from the fight against deforestation. This highlights a second drawback of NAMAs: even NAMAs that effectively move the energy mix away from its BAU track may fail to deliver relevant GHG emission reductions in the specific South American context. On the positive side, though, well-designed NAMAs (here with deforestation-based targets) may deliver substantial emission reductions, without impacting strategic sectors such as energy production. From the AND experience, we can infer that the energy sector may not have the highest emissions reduction potential in South America, due to the weight of forestry and agriculture in the continent's emissions. This assumption is detailed and confirmed in the next paragraph.

www.cma.fr Energy sector contribution to regional climate action: the case of latin America

In this last paragraph, we review the various sources and sinks for greenhouse gases modeled in T-ALyC and their contribution to GHG emission reduction, to contextualize the energy sector's contribution to fulfilling regional climate commitments.

Figure 15 shows GHG emissions, sector by sector, under the least stringent (BAU) and most stringent (Red4All) pledge scenarios, for the whole region. Figure 16 details GHG abatement in the Red4All scenario. Agriculture is the most emitting sector, totaling 47% of regional emissions in 2050 in the BAU scenario (2.9 GtCO2eq out of 6.17 GtCO2eq total emissions). The industry and transport sectors account for 37% of GHG emissions, while the energy sector (oil refining and electricity production) comes third with 12% of total emissions. The cumulative emission reductions achieved by energy, industry, transport, residential and commer-cial sectors together, through modal shift, renewable energy, carbon capture and storage, industrial efficiency, etc. represent 44% of total GHG abatement in 2050 under the Red4All scenario. Meanwhile, the remaining 56% are provided by AFOLU measures (mainly fighting deforestation, and reforestation). It is worth noting that due to the virtuous trend highlighted in paragraph 3.1, energy emissions already decrease in Business-as-Usual conditions, and that energy is the only sector showing this downward trend. The emissions reduction patterns considered here are radically different from the situation in Europe, where energy is foreseen as the main contributor to emissions reduction by 2050 (European Commission, 2011). In Central and South America, due to the overwhelming weight of AFOLU emissions, decarbonizing energy production and consumption is no longer the least expensive or most efficient tool to reduce GHG emissions. In fact, it would fall short of delivering more than 50% emission reduction, even at a prohibitive cost, and the target set here for 2050 -a 40% reduction-is not that far from that limit. GHG emission reductions in South America should therefore be considered from a very different viewpoint: energy is not the easiest way to achieve emissions reduction because it is not the main problem; forestry, on the other hand, remains a long-run carbon sink whose management options are the focus of active research, in terms of both technology and policy aspects (Arima et al., 2014;Asner et al., 2014). In the whole world, it is estimated that deforestation and forest degradation account for 17% of GHG emissions (IPCC, 2007) and these activities are already seen as a 'low-hanging fruit' in the fight against climate change [START_REF] Stern | The Economics of Climate Change: The Stern Review[END_REF], (Buizer et al., 2014). The present work tends to confirm this trend in the case of South America.

www.cma.fr Energy sector contribution to regional climate action: the case of latin America

IV -Conclusions and policy implications

This paper analyzed the energy sector's contribution to GHG emissions reduction in the UNFCCC framework. We outlined South America's energy sector potential for GHG abatement and the evolutions required to realize this potential. We investigated this issue by means of a bottom-up, longterm optimization model, based on the TIMES paradigm yet specifically designed for South America: the TIMES-América Latina y el Caribe model, or T-ALyC. We compared four scenarios based on current national communications to the UNFCCC: a Business-As-Usual case, a BraChi scenario where only Brazil and Chile's pledges apply, a NAMAs scenario including all communicated NAMAs, and a hypothetic Red4All scenario where all countries except Venezuela would make Brazil-like commitments to reduce their GHG emissions by 40% below their baseline by 2050. In our projections, energy accounts for nearly 20% of emission reductions in the most stringent (Red4All) scenario, with AFOLU providing 56% of these reductions in 2050. We find that energy is not the main contributor to emission reductions in South America for two main reasons: first, in our baseline, long-term economic optimization already leads to a decarbonization of the electricity sector. Further decarbonization can be achieved by shifting primary energy consumption by end-use sectors such as industry or transport. Second, the weight of deforestation and land degradation in the continent's GHG balance is considerable, even today, and it is more economically viable to curb this trend than to decarbonize a fairly clean energy mix. As a consequence, the impact of national pledges on the energy sector is real, yet feedback in terms of GHG abatement remains limited. We find that while pledges by Brazil and Chile impact the whole continent's energy trade by undermining oil and coal competitiveness, the added impact of Colombia's NAMAs is low, since national targets do not go far beyond our BAU trend. In Peru and Ecuador, NAMAs' impact on the energy system is more significant, yet forestry-aimed NAMAs alone deliver 90% of the sub-region's GHG abatement. However, the overall impact of NAMAs on Peru and Ecuador is strong, leading to significant emission reductions compared to BAU (35%). We also showed that a sustained drop in international oil prices due to e.g. an international climate agreement, could negatively impact the continent's emissions if South America did not commit to such an agreement, as oil exports would be redirected towards internal consumption and displace renewable energy sources. It is worth noting that such a drop would also have dramatic consequences on the Venezuelan economy, which relies quite heavily on oil exports.

The policy implications of these results, as developed in the results section, are many. We summarize four of them here. First, our results confirm the initial statement that South American climate-energy issues merit ad hoc modeling at a regional scale, since the countries on the continent share features that are quite different from the rest of the world, i.e. a highly renewable energy mix, very high renewable energy potentials along with high deforestation and degradation rates, which call for regional answers to regional issues. Second, in light of our results, that is, considering a first-order optimum that leaves aside energy markets and short-term decision-making, clean energy generation appears to be an economically viable option for South America. It is beyond the range of our modeling approach to take non-optimality factors into account to determine a second-best optimum; however, these first results suggest that heavy subsidies on fossil fuels such as those that exist in Venezuela, Argentina and Peru, may not move in the direction of economic optimality, in addition to their environmental inefficiency. Third, the significance of Brazil in South America's fight against climate change is incontestable, since its decisions already drive relevant changes in its neighbors' energy mixes. Last, and most important, we confirm that, in contrast to Annex I countries, energy cannot be the main focus of efforts to fight global warming in South America because it is not the continent's main problem. In South America, deforestation and land degradation are not only part of the climate issue: they make up the bulk of it.

The importance of deforestation also points to one limitation of our study: although we considered energy production and transformation in a very detailed way, our representation is more limited when it comes to AFOLU, due to the weak link between energy and e.g. reforestation. Further investigation of energy and AFOLU interactions in a climate context would require internalizing a bottom-up approach of the forestry sector, building on work such as e.g. (Overmars et al., 2014). Following another research line, integrating our results back into the global TIAM energy model would extend the intuitions we developed here on the role of oil in an interesting way, providing dynamic oil price feedback based on the possible results of climate talks, rather than a mere sensitivity analysis. Last, one major component of the climate-energy nexus that has not been touched on here is the adaptation issue: beyond mitigation, how to prepare a strongly renewable, climate-sensitive energy mix to tackle uncertain climate change effects? This issue is currently being worked on, and will form the basis of another publication.

www.cma.fr Energy sector contribution to regional climate action: the case of latin America

VI -Bibliography

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Hof

Matthews

Figure 1 :

 1 Figure 1: Schematic description of T-ALyC's RES

Figure 3

 3 Figure3shows the regional impact of climate scenarios in terms of emission reductions. Pledges by Brazil and Chile alone achieve a reduction of 1.08 GtCO2eq, equal to 17.5% below BAU projection, which is nearly half of the reductions achieved in the most stringent scenario. The NAMAs scenario results in an emissions reduction of 23.6% below BAU in 2050 (4.8 GtCO2eq instead of 6.2), yet 2050 emissions are still above 2010 figures, and the upward trend is not curbed. In the case of national commitments to reduce emissions by at least 40% from all countries (minus Venezuela), a 35.3% emission reduction below BAU is achieved in the region. 2050 GHG emissions are below 2010 levels, yet they climb up again from 2020 onwards, mainly due to Venezuelan emissions.

Figure 3 :

 3 Figure 3: GHG emissions in CSA under BAU, NAMAs and Red4All scenarios

Figure 4 :

 4 Figure 4: Electricity production in South America, 2012-2050 (Business-As-Usual)

  Fossil fuels are replaced by hydropower, geothermal electricity and biomass-based production. The lower reliance on solar electricity in 2050 is mostly due to Brazil and Argentina and Colombia, and occurs for two main reasons. First, once oil has been completely removed from the electricity mix, the model installs BECCS technologies instead of solar panels to further decarbonize its electricity. Second, electricity prices rise slightly under climate constraint, and we reach a tipping point between decentralized PV and centralized, midprice hydro production. This is a manifestation of the 'razor edge effect' of linear optimization models, as documented by e.g.(Labriet et al., 2010).

Figure 5 :

 5 Figure 5: Modification of the power mix relative to BAU in BraChi, NAMAs and Red4All scenarios

Figure 6 :

 6 Figure 6: Deviation from the BraChi power mix in COL and AND in the NAMAs scenario, for three price scenarios

  First, Venezuelan crude oil exports, which make up the bulk of South American exports, are capped in our model at 24 PJ/year (approx. 573 Mtoe/yr) to avoid over-unrealistic export volumes, since global oil prices are static in this version of T-ALyC. Due to capacity expansion inertia, this threshold is reached in 2030, marking a clear break in the upward trend. Second, after two decades of oil bounty, exporting towards its neighbors and the rest of the world, Brazil itself starts importing oil, dragging Argentina and Uruguay along.

Figure 7 :

 7 Figure 7: Primary energy production under BAU assumptions

Figure 9 :

 9 Figure 9: Change in primary energy consumption in CSA with low global oil prices Brazilian pledges drive regional decarbonization

Figure 11 :

 11 Figure 11: fossil fuel consumption in 2010 and 2050 (BAU)

Figure 12 :

 12 Figure 12: Modification of the primary energy mix relative to BAU in BraChi, NAMAs and Red4All scenarios

  Figure 16 allows us to focus specifically on emissions absorption. The gray shading concerns absorption in the energy sector, green shows forestry options and red indicates GHG abatement options deployed in end-use sectors. The GHG abatement displayed here only relates to specific abatement-targeted measures as described in the legend, i.e. it does not consider emission reductions through e.g. fuel shift, demand reduction or efficiency improvements. As a consequence, the origin of emissions reduction in the transport and industry sectors is not captured well. The role of carbon storage in reducing energy emissions, however, appears clearly: together, enhanced Oil & Gas Recovery and Storage in depleted fields account for 200 MtCO2eq of emission reductions, i.e. more than 40% of all energybound emission reductions. Proper handling of flared gases adds another 36.5 MtCO2eq, with the remaining reductions due to further decarbonization of the energy mix. What also clearly emerges is the key role played by forestry in GHG emissions abatement, with 1, "Agriculture" in T-ALyC aggregates all AFOLU emissions.

Figure 15 :

 15 Figure 15: GHG net emissions by sector, under BAU and Red4All scenarios

  , A.F., den Elzen, M.G.J., Roelfsema, M., 2013. The effect of updated pledges and business-as-usual projec-

  Loulou, R., Labriet, M., 2008. ETSAP-TIAM: the TIMES integrated assessment model Part I: Model structure. Comput. Manag.

-GHG emissions and storage in T-ALyC

	W Working Paper N°2016-02-20	Energy sector contribution to regional climate action: the case of latin America
	2-2 The emission structure in South America is quite different from the rest of the world. Brazil's national emission inventory reports GHG emissions from the energy sector that amount to only 15% of total national emissions (Brazilian Ministry of Science and Technology, 2010). By comparison, energy emissions for the European Union at the same date accounted for 80% of total emissions 2 (European Commission, 2014). This is mainly due to AFOLU: while in 2005 the Land-use, Land Use Change and Forestry sector in Europe was a net sink at 281 Mt While some emission reduction potentials are directly linked to the amount of emissions (e.g. thermal de-struction of N2O emissions from the Nitric Acid In-dustry, or the fight against deforestation), some potentials are only partially related to such emissions -e.g. reforestation -or totally unrelated -e.g. stor-age in deep aquifers. In the case of forestry-based options, the potentials and associated costs were calibrated on external sources such as (Asner et al., 2014; Brazilian Ministry of Science and Technology, 2010; Elberg Nielsen et al., 2014; Gonzalez Arenas et al., 2011; Ministerio de Ambiente de Colombia, 2012; CO2eq, the same sector in Brazil contributed up to 1,329 Mt CO2eq to national emissions. AFOLU emissions are thus not explicitly energy-related, yet they can impact the energy system through climate pledges. Faced with an emission-reduction objec-tive, planners could choose to spend the money either on emission reductions in the energy-pro-Ministerio de Ambiente del Perú, 2010; Ministerio del Ambiente del Ecuador, 2012, 2011; Ministerio del Medio Ambiente de Chile, 2011; Ministerio del Medio Ambiente de Uruguay, 2010; Nepstad et al., 2009; 2007; Secretaria de Ambiente del Paraguay, 2011; Secretaria de Ambiente de la República Argentina,	Smith et al., 2014; Viceministerio del Medio Ambiente duction sector, or on dedicated non-energy meas-de Bolivia, 2009). We separate measures related to ures in e.g. the AFOLU or waste sectors. In the the fight against deforestation, calibrated on national case of waste-linked emissions, emission reduc-baseline projections for deforestation, from afforesta-tions can even lead to energy production if landfill tion-related measures, whose potential is linked to gases are retrieved and used for electricity gener-the available surface area. This area depends on the ation. Available options in AFOLU include curbing amount of forest-free land, and on the competition deforestation, reforestation measures (re-establish-between afforestation and agriculture or other pro-ment of a forest depleted by deforestation) and af-ductive activities. forestation (creation of new forest areas). See (Smith et al., 2014) for a complete description of For all other options, we used TIAM costs and po-AFOLU's stakes in relation to global warming. tentials (Ricci and Selosse, 2013) and regionalized the latter based on the T-ALyC regions' extraction Such emissions are taken into account in our potentials and surface areas. The potentials and model through dedicated emission technologies, costs of carbon storage technologies are detailed in with an exogenous calibration based on national Table 2 and Table 3 respectively. CCS option costs communications to the UNFCCC. Figure 2 below summarizes these contributions. include transportation.
	Energy potentials and end-use
	demands are calibrated based
	on a wide variety of sources,			Region description
	including (ALACER, 2013; Gar-cés et al., 2012; Global Energy	AND		Peru, Ecuador
	Observatory, 2013; Hoornweg	ARG		Argentina
	and Bhada-Tata, 2012; IEA, 2014; IER, 2006; IMF, 2014;	BPU		Bolivia, Paraguay, Uruguay
	Riegelhaupt and Chalico,	BSE	Brazil -South and Southeast administrative regions
	2009; Smeets et al., 2007; UN-DESA, 2012; UNEP, 2012; US-EIA, 2014; World Nuclear	BWC CHL	Brazil -North, Northeast and Center administrative regions Chile
	Association, 2008) and na-	COL		Colombia
	tional sources. For this study, prices for energy commodity	CYC		Central America and the Caribbean
	trade with the rest of the world	SUG		Suriname, Guyana, French Guyana
	are based on TIAM endoge-nous trade prices for the Cen-	VEN		Venezuela
	tral and South America region.			Table 1: T-ALyC geographical disaggregation
				www.cma.fr

STORAGE OPTION AND ARG BPU BSE BWC CHL COL CYC SUG VEN Enhanced Oil Recovery

		1,629 2,863 1,732 1,593 7,258 778 1,087 762	369	928
	Storage in depleted fields	5,341 9,389 5,680 5,224 23,798 2,552 3,564 2,498 1,211 3,044
	Enhanced coalbed meth. recov.	171	301	182	168	764	82	114	80	39	98
	Deep saline aquifers	2,598 4,566 2,763 2,541 11,574 1,241 1,733 1,215 589 1,480
	Curbing deforestation	15,506	1	4,905 1,272 12,053	0	3,764	0	0	0
	Afforestation/reforestation	3,299 1,561 756	572 5,424 229 1,258	0	0

Table 2 :

 2

	STORAGE OPTION	COST ($/TCO2)
	Deep saline aquifers (onshore)	5.7
	Deep saline aquifers (offshore)	9.3
	Enhanced Oil Recovery and depleted fields injection (onshore) 5.1
	Enhanced Oil Recovery and depleted fields injection (offshore) 8.2
	Enhanced coalbed methane recovery	4.9
	Curbing deforestation -Step 1	3
	Curbing deforestation -Step 2	6
	Curbing deforestation -Step 3	55
	Afforestation -Step 1	10
	Afforestation -Step 2	25
	Afforestation -Step 3	45

Cumulative storage capacity (2010-2050) for T-ALyC carbon storage options (MtCO2)

Table 3 :

 3

	W Working Paper N°2016-02-20

Cost of carbon storage technologies ($2000/tCO2)

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The elctric mobility option, although much discussed in literature, is actually not studied here, due to model limitations. It could bring interesting further research venues, though.

As a reminder, Brazil alone represents more than 40% of the continent's GDP, making it a giant in the region.

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Acknowledgements

VI

Bibliography


Paolo Baldan

Filippo Bonchi

Fabio Gadducci

Giacoma V Monreale

Encoding Synchronous Interactions using Labelled Petri Nets

Keywords: Communicating sequential processes (CSP), labelled Petri nets, net encoding of processes, synchronous interaction

We present an encoding of (bound) CSP processes with replication into Petri nets with labelled transitions. Through the encoding, the firing semantics of Petri nets models the standard operational semantics of CSP processes, which is both preserved and reflected. This correspondence allows for describing by net semantics the standard CSP observational equivalences. Since the encoding is modular with respect to process syntax, the paper puts on a firm ground the technology transfer between the two formalisms, e.g. recasting into the CSP framework wellestablished results like decidability of coverability for nets. This work complements previous results concerning the encoding of asynchronous interactions, thus witnessing the expressiveness of (open) labelled nets in modelling process calculi with alternative communication patterns.

Introduction

Petri nets [START_REF] Reisig | Understanding Petri Nets[END_REF] are among the most widely used formalisms for the visual specification of concurrent and distributed systems. Their appeal lies in the ease of use as well as in the expressiveness. Indeed, their graphical presentation allows for a simple description of possibly complex interaction patterns, in such a way that both synchronous and asynchronous features are plainly represented. Also, in a Petri net the behavioural relations between computational steps, such as causal dependencies and nondeterministic choices, are explicit and easier to analyse.

These characteristics also favoured Petri nets as the target for the encoding of many textual formalisms, such as different process calculi. This is partly due to the availability of many tools and techniques for the analysis of net behavioural properties, like coverability, boundedness, and deadlock-freedom, so that any suitable encoding might offer the possibility of a fruitful technology transfer. However, it is the same simple and immediate graphical presentation of nets that attracted the attention of researchers, in the hope of clarifying the nature of concurrency and distributivity in the formalism at hand. Indeed, there has been since a long time an interest for the encoding of synchronous calculi such as Milner's CCS. Intuitively, the handshaking communication pattern of CCS and π-calculus can be implemented via nets in such a way that the operational behaviour of a process is (at least) preserved by the encoding [START_REF] Gorrieri | SCONE: A simple calculus of nets[END_REF][START_REF] Devillers | A compositional Petri net translation of general pi-calculus terms[END_REF].

In a recent work we offered a further witness to the flexibility of nets by providing an encoding for asynchronous CCS [START_REF] Baldan | Encoding asynchronous interactions using open Petri nets[END_REF]. More precisely, our encoding preserves the operational behaviour of processes as well as asynchronous bisimilarity, captured by standard net bisimilarity. In order to model the intrinsic reactivity of CCS processes, the encoding resorted to open Petri nets [START_REF] Baldan | Bisimilarity and behaviour-preserving reconfigurations of open Petri nets[END_REF], i.e., nets extended with the possibility of interacting with the environment through an interface. Specifically, the interface consists of a set of places designated as open, where the environment can create and consume tokens. Interfaces were also essential to define composition operations on nets, thus allowing for a modular definition of the encoding. The need of considering reactive extensions of Petri nets in order to have a modular model, with compositional semantics, have been felt by several authors, leading to the Box Calculus [START_REF] Best | The Petri box calculus: a new causal algebra with multi-label communication[END_REF], the Petri net components [START_REF] Kindler | A compositional partial order semantics for Petri net components[END_REF] and other open net models [START_REF] Nielsen | Characterizing behavioural congruences for Petri nets[END_REF][START_REF] Bruni | Connector algebras for C/E and P/T nets' interactions[END_REF], just to mention a few.

This paper aims at further extending our results by moving back to synchronous processes, yet taking into account the broadcast communication pattern, as provided by Hoare's CSP [START_REF] Hoare | Communicating Sequential Processes[END_REF]. More precisely, we identify an expressive fragment of CSP which can be mapped modularly into Petri nets via an encoding that is preserving as well as reflecting the operational semantics. Since most of CSP semantics are based on traces, the encoding is guaranteed to preserve and reflect also the common observational equivalences for the calculus. This allows some immediate technology transfer from nets to processes. For instance, coverability, the maximal degree of parallelism of a process (given by the number of its sub-processes occurring in parallel) and convergence (i.e., the possibility of termination) can be proved to be decidable in the CSP setting. Some of these decidability results seem to be the first of their kind for (bound) CSP processes.

The idea of mapping CSP processes into nets arose early on, see among others [START_REF] Goltz | CSP-programs with individual tokens[END_REF][START_REF] Olderog | Operational Petri net semantics for CCSP[END_REF][START_REF] Degano | An exercise in concurrency: a CSP process as a condition/event system[END_REF]. Conceptually, all these encodings are syntax-driven: each process is split into a family of sequential components, which represent the places of a net, and a (possibly concurrent) semantics for the calculus is thus obtained. As of more recent advances, we are aware of [START_REF] Llorens | Generating a Petri net from a CSP specification: A semantics-based method[END_REF]. There, an on-the-fly algorithm is devised for building (and optimising) a net from a CSP process by exploiting its transition system. In our encoding we followed the spirit of the former proposals, striving for modularity: the encoding itself has a denotational flavor, mapping each operator of the calculus into an operator on nets, and as a consequence preservation and reflection of CSP standard operational semantics are easily stated and proved. We believe that such clarity is due to the identification of the right CSP fragment. Indeed, it is noteworthy that in all the papers mentioned above the recursion of nested parallel processes is not allowed "because the set of places of the generated Petri net would be infinite" [14, p.111]. Our paper lifts such a constraint: our chosen CSP fragment is not finite state, but rather it bounds the number of parallel processes synchronising on the same channel. The paper is structured as follows. Section 2 recalls the syntax and the operational semantics of CSP, while Section 3 introduces labelled nets with interfaces, as well as a suitable algebra for them. The core of the paper is Section 4, which presents the modular encoding from (bound) CSP processes into labelled nets. In Section 5 the encoding is proved to preserve and reflect the operational semantics, and hence the standard observational equivalences of the calculus (such as trace equivalence). The encoding is exploited in Section 6, which provides some examples of its effects on the technology transfer between the two formalisms. Finally, Section 7 discusses some expressiveness issues for the considered models, taking advantage from the encoding, and it draws some conclusions while providing a few pointers to future works.

Communicating Sequential Processes

In this section we briefly review the calculus of Communicating Sequential Processes (CSP) [START_REF] Hoare | Communicating Sequential Processes[END_REF], presenting its syntax and operational semantics. We actually focus on a fragment of the calculus, which will be used throughout the paper.

Definition 1 (CSP processes). Let Σ be the alphabet of communication events, ranged over by a, b, c . . . The set of CSP processes P, ranged over by P, Q, R, . . ., is generated by the grammar in Fig. 1, where X ⊆ Σ is a finite set of events.

The process ST OP cannot perform any event, i.e., it is a deadlocked process. The guarded alternative ⊕ n i=1 a i .P i can perform any event a i , for i ∈ {1, . . . , n}, and then behave as P i . For the sake of simplicity, we assume that ∀j, ∀z. a j = a z . The nondeterministic choice P + Q can behave as either P or Q. The operators ⊕ and + differs for the fact that for ⊕ the choice is external, i.e., it is the environment that determines the branch to be chosen, while for + the choice is internal to the process. The process P | X Q is the parallel composition of P and Q, where the events in X are forced to synchronise, while those in Σ \ X be performed by P and Q independently. The hiding P \X behaves like P except for the fact that the events in X are hidden to the environment, that is, they become internal to the process. Finally, the replication ! a .P can indefinitely perform an event a and spawn a parallel copy of P .

(Alt) j ∈ {1, . . . , n} The guarded alternative is a specialisation of the external choice operator. This restriction does not represent a serious limitation since, as explained in [START_REF] Roscoe | The Theory and Practice of Concurrency[END_REF], it is rare to find a usage of the external choice which cannot be expressed as a guarded alternative. More interestingly, we consider guarded replication in place of recursion. This will be important for ensuring the existence of a finite Petri net encoding for the class of CSP processes considered (see Section 5).

⊕ n i=1 ai.Pi a j -→ Pj (Cho1) P + Q τ -→ P (Cho2) P + Q τ -→ Q (Syn1) P µ -→ P µ ∈ X P |X Q µ -→ P |X Q (Syn2) Q µ -→ Q µ ∈ X P |X Q µ -→ P |X Q (Syn3) P a -→ P Q a -→ Q a ∈ X P |X Q a -→ P |X Q (Hid1) P µ -→ P µ ∈ X P \X µ -→ P \X (
The behaviour of CSP processes, intuitively described above, is formalised in terms of a set of syntax directed rules which axiomatise a transition relation.

Definition 2 (operational semantics of CSP). The labelled transition system (LTS) for CSP processes is the relation →⊆ P × (Σ {τ }) × P inductively defined by the rules in Fig. 2, where we write P µ -→ P for P, µ, P ∈→. We write P s -→ * P for a sequence

P = P 1 µ1 -→ P 2 µ2 -→ . . . µn-1
---→ P with s = µ 1 µ 2 . . . µ n-1 . Moreover, we write P s = ⇒ P when P s -→ * P for some s such that s is obtained from s by removing the τ 's. We write simply P -→ P and P -→ * P instead of P µ -→ P and P s -→ * P , respectively, whenever we are not interested in identifying the labels.

Definition 3 (bound processes). A CSP process P ∈ P is called bound if parallel compositions | X occur under the scope of replications only with X = ∅.

In a bound process only pure parallel composition, without synchronisation, is allowed under the scope of replications. This avoids the possibility of having an unbounded number of parallel components synchronising on the same event. Additionally, a synchronisation under a replication would possibly lead to the generation of an unbounded number of conceptually different names as in ! a .(b.b.ST OP | {b} b.ST OP ). As discussed in Section 4, this fact will be essential for defining a finite encoding of bound CSP processes into Petri nets.

Relying on the LTS defined above several observational semantics can be defined over CSP processes. In this paper, we will focus on the one based on traces, i.e., sequences of visible transitions. Definition 4 (traces). Let P ∈ P be a CSP process. We define traces(P ) = {s ∈ Σ * : ∃Q.

P s = ⇒ Q}.
Traces are exploited to provide a behavioral equivalence for processes.

Definition 5 (trace equivalence). Let P, Q ∈ P be two CSP processes. They are called trace equivalent, written

P = T Q, if traces(P ) = traces(Q).

Labelled Petri Nets with Interfaces

This section reviews labelled Petri nets, i.e., ordinary P/T nets with labelled transitions [START_REF] Reisig | Understanding Petri Nets[END_REF]. Nets are also enriched with interfaces and endowed with composition operators in order to allow for an inductive encoding of CSP processes.

Labelled Petri Nets

Let X ⊕ be the free commutative monoid over a set X. An element m ∈ X ⊕ , a multiset over X, is often viewed as a function m : X → N (the set of natural numbers) that associates a multiplicity with every element of X. We write

m 1 ⊆ m 2 if ∀x ∈ X, m 1 (x) ≤ m 2 (x)
. The symbol 0 denotes the empty multiset. Given f : X → Y we denote its extension to multisets by

f ⊕ : X ⊕ → Y ⊕ .
Hereafter Σ denotes a fixed set over which all nets are labelled. In the encoding of processes into nets, Σ is the set of CSP communication events.

Definition 6 (labelled Petri net).

A labelled Petri net is a tuple N = (S, T, • (.), (.)

• , λ) where S is the set of places, T is the set of transitions, • (.), (.)

• : T → S ⊕ are functions mapping each transition to its pre-and post-set and λ : T → Σ is the labelling of transitions.

The state of a net is given by a marking, i.e., a multiset of places m ∈ S ⊕ . Hereafter, the components of a net N will be assumed S, T , • (.), (.)

• and λ, possibly with subscripts. We will often write • t and t • instead of • (t) and (t)

• .

Definition 7 (net morphism). Let N 1 , N 2 be two labelled nets. A net morphism f : 1.

N 1 → N 2 is a pair of functions f = f S , f T where f S : S 1 → S 2 , f T : T 1 → T 2 satisfy
f ⊕ S ( • t) ⊆ • f T (t) (reflection of pre-set) 2. f ⊕ S (t • ) ⊆ f T (t) • (reflection of post-set) 3. λ 1 (t) = λ 2 (f T (t)) (preservation of labels).
Net morphisms roughly represent the insertion of a net into a context. As a consequence the pre-and post-set of transitions can be larger in the target net.

Example 2. Fig. 3 (left) shows a labelled net. As usual, circles represent places and rectangles transitions. Arrows represent pre-and post-sets of transitions. Bullets in places, referred to as tokens, represent the current marking m of the net. Transition labels are placed inside the corresponding rectangle. For the sake of readability, also some places are provided with an identifier, yet positioned outside of the corresponding circle.

Petri Nets with Interfaces

In order to define the encoding of CSP processes into Petri nets inductively, we equip nets with "handles" for interacting with the environment and define operations for composing them.

Definition 8 (Petri net with interfaces). A Petri net with interfaces is a tuple N = I, O, N, V , where N is a labelled net, I and O are subsets of places, the input and output places, and V is a subset of transitions, the visible transitions.

Hereafter, the components of a net with interfaces N will be assumed to be I, N, O, and V , possibly with subscripts.

The standard operational semantics on Petri nets naturally induces a semantics for nets with interfaces, where the firing of a transition that is not visible is turned into a silent action τ . This is expressed by the rules in Fig. 4.

Graphically, a net with interfaces is depicted as a net with input interface on the left and output interface on the right, marked with incoming and outgoing dotted arrows, respectively. Places in the input and output interface are in blue and red, respectively (grey if in b&w) while internal places are white. Moreover, visible transitions are green (grey if in b&w) and hidden ones are white. As in the case of CSP processes, we write m s -→ * m when there is a sequence

(vis) m = • t ⊕ m t ∈ V m λ(t) --→ t • ⊕ m (hid) m = • t ⊕ m t ∈ T \ V m τ -→ t • ⊕ m
m = m 1 µ1 -→ m 2 µ2 -→ . . . µn-1 ---→ m with s = µ 1 µ 2 . . . µ n-1 . We also write m s = ⇒ m when m s -→ * m
for some s such that s is obtained from s by removing the τ 's. We next define suitable composition operators on nets with interfaces.

Definition 9 (sequential composition). Let N 1 and N 2 be nets with interfaces such that

O 1 = I 2 = S 1 ∩ S 2 and T 1 ∩ T 2 = ∅. Their sequential composition is the net with interfaces N 1 •N 2 = I 1 , O 2 , N, V 1 ∪V 2 ,
where N is the pointwise union N 1 ∪ N 2 , with the obvious pre-set, post-set and labelling functions.

Intuitively, the sequential composition N 1 • N 2 is obtained by taking the disjoint union of the nets underlying N 1 and N 2 , and gluing the output places of N 1 with the corresponding input places of N 2 . For the sake of presentation, it is convenient to assume that the two nets intersect only on the input/output interfaces and take the plain union. This could require some alpha-renaming.

In the following, given a net with interfaces N and a set X ⊆ Σ, we denote by V X = {t ∈ V : λ(t) ∈ X} the set of transitions labelled with an event in X.

Definition 10 (synchronised parallel composition). Let N 1 and N 2 be nets with interfaces such that S 1 ∩ S 2 = ∅ and T 1 ∩ T 2 = ∅, and let X ⊆ Σ. Their synchronised parallel composition on X is the net with interfaces

N 1 ⊗ X N 2 = I 1 ∪ I 2 , O 1 ∪ O 2 , N, V , where the set of visible transitions is V = V 1 ⊗ X V 2 = { t 1 , t 2 : t 1 ∈ V X 1 ∧ t 2 ∈ V X 2 ∧ λ 1 (t 1 ) = λ 2 (t 2 )} ∪{ t 1 , * : t 1 ∈ V X 1 ∧ V λ1(t1) 2 = ∅} ∪{ * , t 2 : t 2 ∈ V X 2 ∧ V λ2(t2) 1 = ∅} ∪{t : t ∈ V i \ V X i }
and N = (S, T, • (.), (.)

• , λ) defined as follows

-S = S 1 ∪ S 2 {p} -T = (T 1 \ V 1 ) ∪ (T 2 \ V 2 ) ∪ V -• t = • t if t ∈ T i \ V X i • t 1 ⊕ • t 2 if t = t 1 , t 2 with the convention • * = p -t • = t • if t ∈ T i \ V X i t 1 • ⊕ t 2 • if t = t 1 , t 2 , with the convention * • = 0 -λ(t) =    λ i (t i ) if t ∈ T i \ V X i λ 1 (t 1 ) if t = t 1 , t 2 ∧ t 1 = * λ 2 (t 2 ) if t = t 1 , t 2 ∧ t 2 = * .
We write

N 1 ⊗ N 2 for N 1 ⊗ ∅ N 2 .
Intuitively, the synchronised parallel composition N 1 ⊗ X N 2 is obtained by taking the disjoint union of the nets N 1 and N 2 , except for those visible transitions labelled with a symbol x ∈ X, which are forced to fire synchronously. Concretely, for each pair of transitions t 1 ∈ V 1 and t 2 ∈ V 2 , with identical label in X, a new transition t 1 , t 2 is inserted whose pre-and post-set is obtained as the union of the pre-and post-set of t 1 and t 2 . If a transition t 1 in N 1 has no possibility of synchronising with a transition of N 2 since V 2 does not include transitions with the same label (V λ1(t1) 2

= ∅), it will not be executable in the synchronised product. This is obtained by turning transition t 1 into t 1 , * and adding to its pre-set a new place p, which will never be marked. The same happens for transitions in N 2 that cannot synchronise with any transition in N 1 . An alternative solution, equivalent from the point of view of the behaviour, would be the removal of the dead transitions. We preferred this solution since, when used for the encoding of CSP processes into nets, it will ensure a closer structural correspondence between reducts of a process and the markings of the net encoding. Finally, transitions which are labelled outside X can fire asynchronously and thus are kept unchanged.

Lastly, we introduce an operation for restricting the set of visible transitions of a net. It is called hiding as it has an obvious analogy with the corresponding operation of CSP processes.

Definition 11 (hiding).

Let N be a net with interfaces and let X ⊆ Σ. The hiding of N with respect to X is the net N\X = I, O, N, V where V = V \V X .

Given a net N, the restriction N \ X behaves exactly as N, but transitions labelled in X, which were previously visible, are now hidden.

When a starting state is fixed, nets are called marked.

Definition 12 (marked nets).

A marked net with interface N is a pair N, m , where N is a net with interfaces and m ∈ S ⊕ is the initial marking.

For marked nets we can consider the language of traces starting from the initial marking and the corresponding equivalence. After building the net encoding of a CSP process, we need to mark its input places in order to fix the initial state. The following operation will then be used.

Definition 14 (closing).

Let N be a net with interfaces. We denote by Cl (N) the marked net with interfaces ∅, O, N, V , I .

From Processes to Nets

This section introduces an encoding for CSP processes into nets with interfaces. It is defined inductively by exploiting the composition operators for nets introduced in Section 3. As anticipated, the encoding is restricted to bound processes.

The encoding relies on a set of constant nets, depicted in Fig. 5, which are combined using the composition operators on nets. The net stop in Fig. 5(a) consists of a single place. The net repl a I in Fig. 5(b), where a ∈ Σ and I = {p 1 , . . . , p n }, by repeated firing of transition a allows for an arbitrary number of "parallel activations" of the net which follows. This will be used as a combinator for replication. The set I is the set of input places of the encoding of the process under the replication operator. The net ⊕ n i=1 a i I i in Fig. 5(c), where a i ∈ Σ and each I i is a set of places, is intended to provide a combinator for the guarded alternative. It consists of n transitions, labelled a 1 ,. . . , a n , all competing for the token in their common pre-set. Each transition a i has I i = {p i1 , . . . , p imi } as post-set, corresponding to the input places of the encoding of the continuation of a i . Finally, the net sum I1∪I2 in Fig. 5(d) is a combinator for nondeterministic (internal) choice. As above, I 1 = {p 1 , . . . , p n } and I 2 = {q 1 , . . . , q n } are sets of places which are the input places of the encodings of the processes involved in the choice. Note that the two transitions are hidden, so by definition of the operational semantics they will be turned into silent actions τ . Hence the label σ ∈ Σ, fixed for the hidden transitions of the internal choice, is totally irrelevant.

Definition 15 (encoding for processes). Let P be a bound process. The encoding of P , denoted by P , is defined as P = Cl (|P |), where |.| is given inductively according to the rules in Fig. 6.

The encoding of a process P is obtained by composing the encoding of its subprocesses and finally marking the input places. It therefore contains one place for each operator !, +, ⊕ and process ST OP of P . Some additional places are inserted by the synchronised parallel composition of nets in order to keep some components inactive (see Definition 10). Note that, in the following examples, we avoid to represent such places when they are isolated. Recall that whenever two components are in a synchronised parallel composition a transition is inserted for each possible synchronisation, i.e., for each pair of events with the same name. Observe that the second a-labelled transition in the encoding of Q cannot fire since after the firing of the first a-labelled transition, place δ is emptied and never filled again. This is consistent with the operational semantics of CSP where Q a -→ a.ST OP | {a} ST OP , in such a way that the remaining occurrence of a cannot be executed since it has no counterpart in the parallel subprocess. a non-trivial parallel synchronised product (where synchronisation is on a nonempty set of events) under the scope of a replication. The net R in Fig. 8 (d) is obtained by closing the net |R|, which in turn is the sequential composition of repl b {α,δ} with |Q|. Notice that the b-labelled transition can fire any number of times, thus generating an unbounded number of tokens in α and δ. Hence also the second a-labelled transition has the opportunity of being fired, in a way which disagree with the semantics of the CSP process.

Now consider the process

R =! b .Q =! b .(a.a.ST OP | {a} a.ST OP ), that is the process Q inserted in a replication. Observe that R is not bound as it contains |ST OP | = stop |⊕ n i=1 ai.Pi| = ⊕ n i=1 aiI |P i | • ( n i=1 |Pi|) |P + Q| = sumI |P | ∪I |Q| • (|P | ⊗ |Q|) |!a.P | = repl a I |P | • |P | |P \X| = |P | \X |P |X Q| = |P | ⊗X |Q|
Roughly speaking, the above problem arises since tokens corresponding to different occurrences of the replicated process are mixed in an improper way. Solving the problem by a different encoding, where each occurrence of a process involved in a replication corresponds to a different subnet in the encoding, would lead to an infinite net for non-bound processes.

Relating CSP and Labelled Nets

In this section we show that any bound CSP process and its net encoding behave essentially in the same way. More precisely, the net encoding of processes preserves and reflects process transitions, and, consequently, the standard behavioural CSP equivalences such as, for instance, trace equivalence.

In order to state these results, we first need to establish a correspondence between the processes reachable from P , hereafter denoted by the set reach(P ) = {Q : P -→ * Q}, and the markings of P . The encoding of a bound process P is inductively defined as the composition of the encoding of its subprocesses. Note that, by definition of the CSP operational semantics, whenever a process P performs a transition to P , the process P is obtained from P by replacing a subprocess with its reduct. Then, it is easy to see that the encoding of those processes reachable from P can be mapped to subnets of P .

Lemma 1 (reachable processes as subnets). Let P be a bound process and let Q be a subprocess of P or a process reachable from P . Let N P and N Q be the labelled nets underlying the encodings P and Q , respectively. Then, a net morphism f Q,P : N Q → N P can by uniquely chosen.

The proof relies on the fact that given a subprocess Q of a process P , a mapping between the net underlying the encoding Q into the one underlying P can be obtained by the inductive definition of the encoding. Hence, each subprocess of P corresponds to a subnet of P . Using this fact, it is not difficult to prove that also the encoding of a process reachable from P can be mapped to a subnet of P . In fact, the processes in reach(P ) consist of compositions of reducts of subprocesses of P , where, due to replication, for some reducts we may have several parallel copies. The encodings of these copies, since by definition they do not synchronise on any event, can be mapped to the same subnet.

By using the lemma above, we can easily define a correspondence between the processes belonging to reach(P ) and the markings of P . Definition 16. Let P be a bound process. The function m P : reach(P ) → S ⊕ P maps any process Q ∈ reach(P ) into the marking f ⊕ Q,P (m Q ).

Once established that each process reachable from a bound process P identifies a marking in the net P , we can state the two main correspondence results of this section.

Theorem 1. Let P be a bound process and let Q ∈ reach(P ). Then 1

. if Q µ -→ R then m P (Q) µ -→ m P (R) in P ; 2. if m P (Q) µ -→ m in P then Q µ -→ R with m = m P (R).
The result establishes a bijection between the labelled transitions performed by any process Q ∈ reach(P ) and the transition firings in the net P from the marking m P (Q).

Such a bijection can then be lifted to a fundamental correspondence between the trace semantics of processes and of their encodings. We have a correspondence also between the transitions of Q and those of its net encoding. Therefore, it is easy to conclude that the nets are trace equivalent.

Some Hints About Technology Transfer

The encoding of bound CSP processes into labelled nets enables to transfer results concerning expressiveness and tractability from one formalism to the other, as it was the case for the net encoding of CCS in [START_REF] Baldan | Encoding asynchronous interactions using open Petri nets[END_REF].

Observe that trace equivalence is obviously undecidable for both bound CSP processes and Petri nets (since they include as a fragment the basic parallel processes for which trace equivalence is known to be undecidable [START_REF] Hirshfeld | Petri nets and the equivalence problem[END_REF]). Still, even though this does not give new insights, we note that by using the encoding, the undecidability of trace equivalence for Petri nets can be also deduced directly from the undecidability of trace equivalence for bound CSP.

Reachability, namely the possibility of reaching a given process Q via a sequence of transitions from a start process P , is not a particularly interesting property for CSP. Since during process evolution the number of parallel components can only increase, the property turns out to be decidable. Indeed, in order to establish whether Q is reachable it suffices to consider the fragment of the labelled transition system including the processes reachable from P having a number of parallel subprocesses bounded by that of Q. It is instead more interesting the reachability under the garbage collection of ST OP : it breaks the monotonicity mentioned above, and the removal itself is not trivial. In fact, P | X ST OP is equivalent to P only when X does not include channel names on which P can synchronise. E.g., think of the process a.ST OP which can perform an a-labelled transition while a.ST OP | {a} ST OP is deadlocked.

Alternatively one can consider control state reachability, i.e., the reachability of a configuration including a given subprocess. In this last case, it is sufficient to consider net coverability. It is folklore that the control state reachability problem is undecidable for full CSP, while the corresponding property of coverability is known to be decidable for Petri nets [START_REF] Esparza | Decidability issues for Petri nets -a survey[END_REF]. By exploiting the encoding, decidability of coverability can be transferred from Petri nets to bound processes.

Corollary 1 (reachability). Let P, Q be bound processes. The problem of establishing whether there exists bound process R such that P -→ * R and Q is a sub-process of R is decidable.

Thanks to the correspondence between processes reachable from a process P and reachable markings in the net encoding of P , decidability of boundedness in Petri nets [START_REF] Esparza | Decidability issues for Petri nets -a survey[END_REF] implies that it is possible to determine whether a CSP process has a finite number of states.

Corollary 2 (finite state). Let P be a bound process. It is decidable whether P has a finite number of reachable states.

Again, the property of being finite state can be more interesting for CSP processes when working up to garbage collection of useless STOP parallel components. It can be seen that this property is naturally captured by the boundedness of the subset of places of P not corresponding to STOP processes.

Analogously, it is possible to identify an upper bound to the degree of parallelism of a bound CSP process, i.e., to the number of parallel subcomponents of a process during its evolution. More precisely, define the structural degree of a CSP process P as sdeg(P | X Q) = sdeg(P ) + sdeg(Q) and sdeg(P ) = 1 otherwise. Then the degree of P is deg(P ) = sup{sdeg(P ) : P → * P }. The close correspondence between deg(P ) and the maximal total number of tokens in the reachable markings of P immediately leads to the following result.

Corollary 3 (parallelism). Let P be a bound process. The problem of determining whether deg(P ) is finite is decidable. Moreover, for any given k ∈ N, it is decidable whether deg(P ) ≤ k.

A classical property in the analysis of the expressiveness of process calculi is convergence, i.e., the existence of a terminating computation. We recall such notion below, according to [START_REF] Busi | Comparing recursion, replication, and iteration in process calculi[END_REF].

Definition 17 (convergence). A process P is called convergent if there exists Q such that P -→ * Q →.

Convergence of a bound process can be reduced to the existence of a deadlock in its encoding, a property which is known to be decidable for Petri nets [START_REF] Esparza | Decidability issues for Petri nets -a survey[END_REF].

Corollary 4 (convergence). Convergence is decidable for bound processes.

Conclusions and Further Works

In this work we have identified a fragment of CSP, consisting of the so-called bound processes, that can be encoded into (labelled) Petri nets. The encoding preserves and reflects the (strong) transitions of the process calculus and, consequently, the whole spectrum of (both strong and weak) behavioural equivalences definable on the transition system of CSP processes. Furthermore, the encoding is syntax-driven, hence modular, mapping each process operator into a suitable one for labelled nets with interfaces. As far as we know, this is a main improvement with respect to former proposals.

Interfaces are in fact the key ingredient to achieve modularity: they are needed in defining the net operators upon which our encoding lays its foundations. Reactive extensions of Petri nets, endowed with means for interacting with the environment [START_REF] Best | The Petri box calculus: a new causal algebra with multi-label communication[END_REF][START_REF] Kindler | A compositional partial order semantics for Petri net components[END_REF][START_REF] Baldan | Bisimilarity and behaviour-preserving reconfigurations of open Petri nets[END_REF][START_REF] Bruni | Connector algebras for C/E and P/T nets' interactions[END_REF], naturally arise as extensions of nets allowing for compositional reasoning. This feature plays a key role for modelling various brands of process calculi. Indeed, in [START_REF] Baldan | Encoding asynchronous interactions using open Petri nets[END_REF] they were pivotal in the encoding of an asynchronous fragment of CCS into open nets. Interestingly enough, asynchronous interactions are captured by a form of composition where net components interact only over places, while in this paper the synchronous interaction is realised by letting net components interact over an interface consisting of transitions. This should have been intuitively expected, since in Petri nets the token flow is eminently asynchronous, while transitions synchronise different token flows.

Therefore, our results confirm that (open) Petri nets can accommodate both asynchronous message passing and barrier synchronisation. In principle, this leaves space for a calculus combining both characteristics, endowed with a direct encoding into nets. This would take us back in full circle, since this calculus would trace its roots on some early proposals for net encoding of processes [START_REF] Olderog | Operational Petri net semantics for CCSP[END_REF].

Fig. 1 .

 1 Fig. 1. CSP processes.

Example 1 .

 1 Consider the processes P = a.(d.b.ST OP \d) ⊕ b.a.ST OP and Q = (c.a.ST OP | {c} c.b.ST OP )\c. It is easy to see that traces(P ) = traces(Q) = { , a, ab, b, ba}. Hence they are trace equivalent.

for any t ∈ T 1 :Fig. 3 .

 13 Fig. 3. Graphical representation of labelled nets, the rightmost with interfaces.

Fig. 4 .Example 3 .

 43 Fig. 4. Operational semantics of nets with interfaces.

Definition 13 (

 13 traces). Let N be a marked net with interfaces. Its set of traces is traces(N) = {s ∈ Σ * : ∃n. m s = ⇒ n}. Two marked nets with interfaces N 1 and N 2 are trace equivalent, written N 1 = T N 2 , if traces(N 1 ) = traces(N 2 ).

sumI 1 ∪I 2 Fig. 5 .

 25 Fig. 5. The constant nets stop, repl a I , ⊕ n i=1 ai I i and sumI 1 ∪I 2 .

Example 4 (

 4 prefix and parallel synchronised processes). Consider the process P = (a.c.ST OP ⊕ b.d.ST OP ) | {d} c.d.ST OP . Its encoding is depicted in Fig. 7 (right), where input and output interfaces are empty and all transitions are visible. It is obtained by closing the net |P |, the result of the parallel composition, synchronised on d, of the encodings |a.c.ST OP ⊕ b.d.ST OP | and |c.d.ST OP |, in turn depicted in the left part of Fig. 7. More precisely, the net on the upper part illustrates |a.c.ST OP ⊕ b.d.ST OP |. The places ν and σ represent the subnets encoding the ST OP processes (those reached after the events c and d, respectively). The subnet rooted at place δ is the encoding of the subprocess c.ST OP . Analogously, the subnet rooted γ is the encoding of the subprocess d.ST OP . The encoding of the subprocess a.c.ST OP ⊕ b.d.ST OP is obtained by sequentially composing the net a.I {δ} ⊕ b.I {γ} with |c.ST OP | ⊗ |d.ST OP |. The net in the lower part represents the encoding |c.d.ST OP | of c.d.ST OP . Example 5 (bound processes). Consider the process Q = a.a.ST OP | {a} a.ST OP . The encodings |a.a.ST OP | and |a.ST OP | are depicted in Fig. 8(a) and (b). The encoding |Q| is obtained as their parallel composition, synchronised on a, as shown in Fig. 8(c). Each transition labelled by a of |a.a.ST OP | is "combined" with any other transition labelled by a in |a.ST OP |.

Fig. 6 .Fig. 7 .

 67 Fig. 6. Encoding for CSP processes.

Fig. 8 .

 8 Fig. 8. Process encodings.

Fig. 9 .

 9 Fig. 9. Net encoding the process (d.a.b.ST OP )\d ⊕ b.a.ST OP .

Theorem 2 .Example 6 .

 26 Let P , Q be bound processes. Then P = T Q if and only if P = T Q . Consider the processes P = a.(d.b.ST OP \d) ⊕ b.a.ST OP and Q = (c.a.ST OP | {c} c.b.ST OP )\c, of Example 1. The encoding of P is in Fig. 9, while the encoding of Q is the net in Fig. 3 (right), once the interfaces are removed. Note that there is a correspondence between the labelled transitions of each process and those of its encoding. For instance, P a → d.b.ST OP \d corresponds to m P (P ) = {α} a -→ {γ} = m P (d.b.ST OP \d). The transition d.b.ST OP \d τ -→ b.ST OP \d corresponds to m P (d.b.ST OP \d) = {γ} τ -→ {σ} = m P (b.ST OP \d) and b.ST OP \d b -→ ST OP \d to m P (b.ST OP \d) = {σ} b -→ {ρ} = m P (ST OP \d). Moreover, P b -→ a.ST OP corresponds to m P (P ) = {α} b -→ {δ} = m P (a.ST OP ), and finally a.ST OP a -→ ST OP to m P (a.ST OP ) = {δ} a -→ {ν} = m P (ST OP ).

Acknowledgements. We are grateful to the referees for their insightful suggestions on the submitted version of the paper, and, in particular, for pointing out the relevance of control state reachability in the analysis of CSP processes.