Abstract
The relation between process calculi and Petri nets, two fundamental models of concurrency, has been widely investigated. Many proposals exist for encoding process calculi into Petri nets while preserving some behavioural features of interest. We recently introduced a framework where a net encoding can be defined uniformly for calculi with different communication patterns, including synchronous two-party, multi-party, and asynchronous communication. The encoding preserves and reflects several behavioural semantics, notably bisimulation equivalence. The situation is less immediate for asynchronous calculi and trace semantics: considering traces that arise when viewing asynchronous calculi as a fragment of the synchronous ones, trace equivalence is not reflected by the encoding. Focusing on CCS, we argue that this phenomenon is related to the imperfect match between trace inclusion and may testing preorder. We consider an alternative labelled transition systems where the latter issue is solved, and we show that, indeed, the corresponding trace semantics is preserved and reflected by the net encoding.
Research partly supported by the MIUR PRIN 2010LHT4KM CINA, the ANR 121S02001 PACE and the University of Padua ANCORE.
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References
Amadio, R., Castellani, I., Sangiorgi, D.: On bisimulations for the asynchronous \(\pi \)-calculus. Theoret. Comput. Sci. 195(2), 291–324 (1998)
Baldan, P., Bonchi, F., Gadducci, F., Monreale, G.: Modular encoding of synchronous and asynchronous interactions using open Petri nets. Sci. Comput. Program. 109, 96–124 (2015)
Baldan, P., Bonchi, F., Gadducci, F., Monreale, G.V.: Encoding synchronous interactions using labelled Petri nets. In: Kühn, E., Pugliese, R. (eds.) COORDINATION 2014. LNCS, vol. 8459, pp. 1–16. Springer, Heidelberg (2014)
Baldan, P., Corradini, A., Ehrig, H., Heckel, R.: Compositional semantics for open Petri nets based on deterministic processes. Math. Struct. Comput. Sci. 15(1), 1–35 (2004)
Baldan, P., Bonchi, F., Gadducci, F., Monreale, G.V.: Concurrency cannot be observed, asynchronously. Math. Struct. Comput. Sci. 25(4), 978–1004 (2015)
Bonchi, F., Gadducci, F., Monreale, G.V.: A general theory of barbs, contexts, and labels. ACM Trans. Comput. Logic 15(4), 35:1–35:27 (2014)
Boreale, M., De Nicola, R., Pugliese, R.: Trace and testing equivalence on asynchronous processes. Inf. Comput. 172(2), 139–164 (2002)
Bruni, R., Melgratti, H.C., Montanari, U., Sobocinski, P.: Connector algebras for C/E and P/T nets’ interactions. Log. Methods Comput. Sci. 9(3), 1–65 (2013)
Busi, N., Gorrieri, R., Zavattaro, G.: Comparing three semantics for Linda-like languages. Theoret. Comput. Sci. 240(1), 49–90 (2000)
Busi, N., Gorrieri, R.: Distributed semantics for the \(\pi \)-calculus based on Petri nets with inhibitor arcs. Logic Algebraic Program. 78(3), 138–162 (2009)
Castellani, I., Hennessy, M.: Testing theories for asynchronous languages. In: Sarukkai, S., Arvind, V. (eds.) FST TCS 1998. LNCS, vol. 1530, pp. 90–102. Springer, Heidelberg (1998)
Degano, P., De Nicola, R., Montanari, U.: CCS is an (augmented) contact free C/E system. In: Zilli, M.V. (ed.) Mathematical Models for the Semantics of Parallelism. LNCS, vol. 280, pp. 144–165. Springer, Heidelberg (1986)
Degano, P., De Nicola, R., Montanari, U.: A distributed operational semantics for CCS based on condition/event systems. Acta Informatica 26(1/2), 59–91 (1988)
Degano, P., Gorrieri, R., Marchetti, S.: An exercise in concurrency: a CSP process as a condition/event system. In: Rozenberg, G. (ed.) APN 1998. LNCS, vol. 340, pp. 85–105. Springer, Heidelberg (1987)
Devillers, R., Klaudel, H., Koutny, M.: A compositional Petri net translation of general \(\pi \)-calculus terms. Formal Aspects Comput. 20(4–5), 429–450 (2008)
Goltz, U.: CCS and Petri nets. In: Guessarian, I. (ed.) Semantics of Systems of Concurrent Processes. LNCS, vol. 469, pp. 334–357. Springer, Heidelberg (1990)
Gorrieri, G., Montanari, U.: SCONE: A simple calculus of nets. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 2–31. Springer, Heidelberg (1990)
Hoare, C.A.R.: Communicating Sequential Processes. Prentice Hall, Upper Saddle River (1985)
Honda, K., Tokoro, M.: An object calculus for asynchronous communication. In: Tokoro, M., Nierstrasz, O., Wegner, P. (eds.) ECOOP 1991. LNCS, vol. 612, pp. 21–51. Springer, Heidelberg (1991)
Jenner, L., Vogler, W.: Fast asynchronous systems in dense time. Theoret. Comput. Sci. 254(1–2), 379–422 (2001)
Leifer, J.J., Milner, R.: Deriving bisimulation congruences for reactive systems. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, p. 243. Springer, Heidelberg (2000)
Milner, R.: Bigraphs for Petri nets. In: Reisig, W., Desel, J., Rozenberg, G. (eds.) Lectures on Concurrency and Petri Nets. LNCS, vol. 3098, pp. 686–701. Springer, Heidelberg (2004)
Montanari, U., Rossi, F.: Contextual nets. Acta Informatica 32(6), 545–596 (1995)
Sassone, V., Sobociński, P.: A congruence for Petri nets. In: Mens, T., Schürr, A., Taentzer, G. (eds.) PNGT 2004. ENTCS, vol. 127, pp. 107–120. Elsevier (2005)
Selinger, P.: Categorical structure of asynchrony. In: Brookes, S., Jung, A., Mislove, M., Scedrov, A. (eds.) MFPS 1999. ENTCS, vol. 20. Elsevier (1999)
Winskel, G.: A new definition of morphism on Petri nets. In: Fontet, M., Mehlhorn, K. (eds.) STACS 1984. LNCS, vol. 166, pp. 140–150. Springer, Heidelberg (1984)
Acknowledgements
We are indebted in many ways to Pierpaolo Degano. Indeed, the earliest exposure of the third author to Petri nets was in a remote cycle of seminars, whose initial lesson was introduced by the quotation in the first page. A scary moment, if there ever was one. Along the years, we all –either as Ph.D. students or later on as co-authors/colleagues/partners in projects– benefited from the insights and availability of Pierpaolo. More technically, we already mentioned his early contributions on net encoding for calculi. In general terms, the insistence on the proof structure of a computation in order to distill a suitable (concurrent) semantics for a calculus, which is typical of the work of Pierpaolo since the early Eighties, has been a fixed star: the modularity of our net encoding spills out of this “commandment”.
We are most grateful to the anonymous reviewers whose suggestions and remarks helped us to improve the paper.
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Baldan, P., Bonchi, F., Gadducci, F., Monreale, G.V. (2015). Asynchronous Traces and Open Petri Nets. In: Bodei, C., Ferrari, G., Priami, C. (eds) Programming Languages with Applications to Biology and Security. Lecture Notes in Computer Science(), vol 9465. Springer, Cham. https://doi.org/10.1007/978-3-319-25527-9_8
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