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On the expressive power of recursion, replication and iteration in process calculi

Published online by Cambridge University Press:  04 December 2009

NADIA BUSI
Affiliation:
Dip. di Scienze dell'Informazione, Univ. di Bologna, Mura A.Zamboni 7, 40127 Bologna, Italy Email: gabbri@cs.unibo.it; zavattar@cs.unibo.it
MAURIZIO GABBRIELLI
Affiliation:
Dip. di Scienze dell'Informazione, Univ. di Bologna, Mura A.Zamboni 7, 40127 Bologna, Italy Email: gabbri@cs.unibo.it; zavattar@cs.unibo.it
GIANLUIGI ZAVATTARO
Affiliation:
Dip. di Scienze dell'Informazione, Univ. di Bologna, Mura A.Zamboni 7, 40127 Bologna, Italy Email: gabbri@cs.unibo.it; zavattar@cs.unibo.it

Abstract

In this paper we investigate the expressive power of three alternative approaches to the definition of infinite behaviours in process calculi, namely, recursive definitions, replication and iteration. We prove several results discriminating between the calculi obtained from a core CCS by adding the three mechanisms mentioned above. These results are derived by considering the decidability of four basic properties: termination (that is, all computations are finite); convergence (that is, the existence of a finite computation); barb (that is, the ability to perform an action on a given channel) and weak bisimulation.

Our results, which are summarised in Table 1, show that the three calculi form a strict expressiveness hierarchy in that: all the properties mentioned are undecidable in CCS with recursion; only termination and barb are decidable in CCS with replication; all the properties are decidable in CCS with iteration.

As a corollary, we also obtain a strict expressiveness hierarchy with respect to weak bisimulation, since there exist weak bisimulation preserving encodings of iteration in replication and of replication in recursion, whereas there are no weak bisimulation preserving encodings in the other directions.

Type
Paper
Copyright
Copyright © Cambridge University Press 2009

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References

Busi, N., Gabbrielli, M. and Zavattaro, G. (2003) Replication vs. Recursive Definitions in Channel Based Calculi. In: Proc. ICALP'03. Springer-Verlag Lecture Notes in Computer Science 2719 133144.Google Scholar
Busi, N., Gabbrielli, M. and Zavattaro, G. (2004) Comparing Recursion, Replication, and Iteration in Process Calculi. In: Proc. ICALP'04. Springer-Verlag Lecture Notes in Computer Science 3142 307319.CrossRefGoogle Scholar
Finkel, A. and Schnoebelen, Ph. (2001) Well-Structured Transition Systems Everywhere! Theoretical Computer Science 256 6392.CrossRefGoogle Scholar
Giambiagi, P., Schneider, G. and Valencia, F. D. (2004) On the Expressiveness of CCS-like Calculi. In: Proceedings of FOSSACS 04. Springer-Verlag Lecture Notes in Computer Science 2987 226240.Google Scholar
Higman, G. (1952) Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 2 236366.Google Scholar
Kanellakis, P. C. and Smolka, S. A. (1990) CCS expressions, finite state processes, and three problems of equivalence. Information and Computation 86 (1)4368.Google Scholar
Milner, R. (1989) Communication and Concurrency, Prentice-Hall.Google Scholar
Milner, R., Parrow, J. and Walker, D. (1992) A calculus of mobile processes. Journal of Information and Computation 100 177.Google Scholar
Minsky, M. L. (1967) Computation: finite and infinite machines, Prentice-Hall.Google Scholar
Nielsen, M., Palamidessi, C. and Valencia, F. D. (2002) On the Expressive Power of Temporal Concurrent Constraint Programming Languages. Proc. of PPDP'02, ACM Press.Google Scholar
Shepherdson, J. C. and Sturgis, J. E. (1963) Computability of recursive functions. Journal of the ACM 10 217255.CrossRefGoogle Scholar
Srba, J. (2003) Undecidability of Weak Bisimilarity for PA-Processes. In: Proc. of DLT'02. Springer-Verlag Lecture Notes in Computer Science 2450 197208.CrossRefGoogle Scholar