Abstract
In the pi-calculus, we consider decidability of certain safety properties expressed in a simple spatial logic. We first introduce a behavioural type system that, given a process P, tries to extract a spatial-behavioural type T, in the form of a ccs term that is logically equivalent to the given process. Using techniques based on well-structured transition systems, we then prove that, for an interesting fragment of the considered logic, satisfiability (T ⊧ φ) is decidable for types. As a consequence of logical equivalence between types and processes, we obtain decidability of this fragment of the logic for all well-typed pi-processes.
Research partly supported by the EU within the FET-GC2 initiative, project Sensoria.
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References
Acciai, L., Boreale, M.: Spatial and behavioral types in the pi-calculus. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 372–386. Springer, Heidelberg (2008) (Full version submitted, 2009)
Acciai, L., Boreale, M.: Deciding safety properties in infinite-state pi-calculus via behavioural types. Extended version, http://gdn.dsi.unifi.it/~acciai/papers/decFull.pdf
Amadio, R., Meyssonnier, C.: On decidability of the control reachability problem in the asynchronous pi-calculus. Nordic Journal of Computing 9(2), 70–101 (2002)
Busi, N., Gabbrielli, M., Zavattaro, G.: Comparing recursion, replication, and iteration in process calculi. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 307–319. Springer, Heidelberg (2004)
Caires, L.: Behavioural and Spatial Observations in a Logic for the pi-Calculus. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 72–89. Springer, Heidelberg (2004)
Caires, L., Cardelli, L.: A spatial logic for concurrency (part I). Inf. Comput. 186(2), 194–235 (2003)
Chaki, S., Rajamani, S.K., Rehof, J.: Types as models: model checking message-passing programs. In: Proc. of POPL 2002, pp. 45–57 (2002)
Finkel, A., Schnoebelen, P.: Well-Structured Transition Systems Everywhere! Theoretical Computer Science 256(1-2), 63–92 (2001)
Higman, G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 2, 326–366 (1952)
Igarashi, A., Kobayashi, N.: A generic type system for the Pi-calculus. Theoretical Computer Science 311(1-3), 121–163 (2004)
Kobayashi, N., Suto, T.: Undecidability of 2-Label BPP Equivalences and behavioural Type Systems for the Pi-Calculus. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 740–751. Springer, Heidelberg (2007)
Kruskal, J.B.: Well-quasi-ordering, the tree theorem, and Vázsonyi’s conjecture. Trans. American Math. Soc. 95, 210–225 (1960)
Milner, R.: The polyadic π-calculus: a tutorial. In: Logic and Algebra of Spec., pp. 203–246 (1993)
Valencia, F., Aranda, J., Versari, C.: On the Expressive Power of Restriction and Priorities in CCS with Replication. In: de Alfaro, L. (ed.) FoSSaCS 2009. LNCS, vol. 5504, pp. 242–256. Springer, Heidelberg (2009)
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Acciai, L., Boreale, M. (2009). Deciding Safety Properties in Infinite-State Pi-Calculus via Behavioural Types. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02930-1_3
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DOI: https://doi.org/10.1007/978-3-642-02930-1_3
Publisher Name: Springer, Berlin, Heidelberg
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