Abstract
We give a compositional event structure semantics of the π-calculus. The main issues to deal with are the communication of free names and the extrusion of bound names. These are the source of the expressiveness of the π-calculus, but they also allow subtle forms of causal dependencies. We show that free name communications can be modeled in terms of “incomplete/potential synchronization” events. On the other hand, we argue that it is not possible to satisfactorily model parallel extrusion within the framework of stable event structures. We propose to model a process as a pair \(({\mathcal E},X)\) where \({\mathcal E}\) is a prime event structure and X is a set of (bound) names. Intuitively, \({\mathcal E}\) encodes the structural causality of the process, while the set X affects the computation on \({\mathcal E}\) so as to capture the causal dependencies introduced by scope extrusion. The correctness of our true concurrent semantics is shown by an operational adequacy theorem with respect to the standard late semantics of the π-calculus.
Chapter PDF
Similar content being viewed by others
References
Boreale, M., Sangiorgi, D.: A fully abstract semantics for causality in the π-calculus. Acta Inf. 35(5), 353–400 (1998)
Bruni, R., Melgratti, H., Montanari, U.: Event Structure Semantics for Nominal Calculi. In: Baier, C., Hermanns, H. (eds.) CONCUR 2006. LNCS, vol. 4137, pp. 295–309. Springer, Heidelberg (2006)
Busi, N., Gorrieri, R.: A Petri Net Semantics for Pi-Calculus. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 145–159. Springer, Heidelberg (1995)
Cattani, G.L., Sewell, P.: Models for name-passing processes: Interleaving and causal. In: Proceedings of 15th LICS, pp. 322–332. IEEE (2000)
Crafa, S., Varacca, D., Yoshida, N.: Compositional Event Structure Semantics for the Internal Pi-Calculus. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 317–332. Springer, Heidelberg (2007)
Danos, V., Krivine, J.: Reversible Communicating Systems. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 292–307. Springer, Heidelberg (2004)
Degano, P., De Nicola, R., Montanari, U.: On the consistency of truly concurrent operational and denotational semantics. In: LICS, pp. 133–141. IEEE (1988)
Degano, P., Priami, C.: Non-interleaving semantics for mobile processes. Theor. Comp. Sci. 216(1-2), 237–270 (1999)
Engelfriet, J.: A multiset semantics for the pi-calculus with replication. Theor. Comp. Sci. 153(1&2), 65–94 (1996)
van Glabbeek, R.J., Plotkin, G.D.: Configuration structures, event structures and petri nets. Theor. Comput. Sci. 410(41), 4111–4159 (2009)
Jagadeesan, L.J., Jagadeesan, R.: Causality and True Concurrency: A Data-Flow Analysis of the Pi-Calculus. In: Alagar, V.S., Nivat, M. (eds.) AMAST 1995. LNCS, vol. 936, pp. 277–291. Springer, Heidelberg (1995)
Lanese, I., Mezzina, C.A., Stefani, J.: Reversing Higher-Order Pi. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 478–493. Springer, Heidelberg (2010)
Montanari, U., Pistore, M.: Concurrent semantics for the pi-calculus. Electr. Notes Theor. Comput. Sci. 1, 411–429 (1995), Proceedings of MFPS 1995
Nielsen, M., Plotkin, G.D., Winskel, G.: Petri nets, event structures and domains, part I. Theor. Comp. Sci. 13(1), 85–108 (1981)
Phillips, I., Ulidowski, I.: Reversibility and models for concurrency. Electr. Notes Theor. Comput. Sci. 192(1), 93–108 (2007), Proceedings of SOS 2007
Sangiorgi, D.: Locality and True-Concurrency in Calculi for Mobile Processes. In: Hagiya, M., Mitchell, J.C. (eds.) TACS 1994. LNCS, vol. 789, pp. 405–424. Springer, Heidelberg (1994)
Varacca, D., Yoshida, N.: Typed event structures and the linear pi-calculus. Theor. Comput. Sci. 411(19), 1949–1973 (2010)
Winskel, G.: Event Structure Semantics for CCS and Related Languages. In: Nielsen, M., Schmidt, E.M. (eds.) ICALP 1982. LNCS, vol. 140, pp. 561–576. Springer, Heidelberg (1982)
Winskel, G.: Event Structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 325–392. Springer, Heidelberg (1987)
Winskel, G., Nielsen, M.: Models for concurrency. In: Handbook of Logic in Computer Science, vol. 4. Clarendon Press (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Crafa, S., Varacca, D., Yoshida, N. (2012). Event Structure Semantics of Parallel Extrusion in the Pi-Calculus. In: Birkedal, L. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2012. Lecture Notes in Computer Science, vol 7213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28729-9_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-28729-9_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28728-2
Online ISBN: 978-3-642-28729-9
eBook Packages: Computer ScienceComputer Science (R0)