Abstract
The Parameterized Model Checking Problem (PMCP) is to decide whether a temporal property holds for a uniform family of systems, U n, comprised of finite, but arbitrarily many, copies of a template process U. Unfortunately, it is undecidable in general [3]. In this paper, we consider the PMCP for systems comprised of processes arranged in a ring that communicate by passing messages via tokens whose values can be updated at most a bounded number of times. Correctness properties are expressed using the stuttering-insensitive linear time logic LTL∖X. For bidirectional rings we show how to reduce reasoning about rings with an arbitrary number of processes to rings with up to a certain finite cutoff number of processes. This immediately yields decidability of the PMCP at hand. We go on to show that for unidirectional rings small cutoffs can be achieved, making the decision procedure provably efficient. As example applications, we consider protocols for the leader election problem.
Research supported in part by NSF grants CCR-020-5483 and CCR-009-8141, and SRC contract 2002-TJ-1026;{emerson, kahlon}@cs.utexas.edu
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abdulla, P., Boujjani, A., Jonsson, B., Nilsson, M.: Handling global conditions in parameterized systems verification. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633. Springer, Heidelberg (1999)
Abdulla, P.A., Jonsson, B.: On the existence of network invariants for verifying parameterized systems. In: Olderog, E.-R., Steffen, B. (eds.) Correct System Design. LNCS, vol. 1710, pp. 180–197. Springer, Heidelberg (1999)
Apt, K., Kozen, D.: Limits for automatic verification of finite-state concurrent systems. Information Processing Letters 15, 307–309 (1986)
Arons, T., Pnueli, A., Ruah, S.: ParameterizedVerification withAutomatically Computed Inductive Assertions. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, Springer, Heidelberg (2001)
Browne, M.C., Clarke, E.M., Grumberg, O.: Reasoning about Networks with Many Identical Finite State Processes. Information and Control 81(1), 13–31 (1989)
Clarke, E.M., Grumberg, O., Jha, S.: Verifying Parameterized Networks using Abstraction and Regular Languages. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 395–407. Springer, Heidelberg (1995)
Emerson, E.A., Kahlon, V.: Reducing Model Checking of the Many to the Few. In: CADE-17. LNCS. Springer, Heidelberg (2000)
Emerson, E.A., Kahlon, V.: Model checking large-scale and parameterized resource allocation systems. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, p. 251. Springer, Heidelberg (2002)
Emerson, E.A., Kahlon, V.: Rapid parameterized model checking of snoopy cache coherence protocols. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 144–159. Springer, Heidelberg (2003)
Emerson, E.A., Kahlon, V.: Model Checking Guarded Protocols. LICS (2003)
Emerson, E.A., Namjoshi, K.S.: Reasoning about Rings. In: POPL, pp. 85–94 (1995)
Emerson, E.A., Namjoshi, K.S.: Automatic Verification of Parameterized Synchronous Systems. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102. Springer, Heidelberg (1996)
German, S.M., Sistla, A.P.: Reasoning about Systems with Many Processes. J. ACMÂ 39(3) (July 1992)
Khurshan, R.P., McMillan, L.: A Structural Induction Theorem for Processes. In: PODC, pp. 239–247 (1989)
Lynch, N.: Distributed Algorithms. Morgan Kaufmann, San Francisco (1996)
Shannon, C.E.: A Universal Turing Machine with Two Internal States. Automata Studies, pp. 157–165. Princeton University Press, Princeton (1956)
Suzuki, I.: Proving properties of a ring of finite state systems. IPL 28, 213–314 (1988)
Wolper, P., Lovinfosse, V.: Verifying Properties of Large Sets of Processes with Network Invariants. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407. Springer, Heidelberg (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Emerson, E.A., Kahlon, V. (2004). Parameterized Model Checking of Ring-Based Message Passing Systems. In: Marcinkowski, J., Tarlecki, A. (eds) Computer Science Logic. CSL 2004. Lecture Notes in Computer Science, vol 3210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30124-0_26
Download citation
DOI: https://doi.org/10.1007/978-3-540-30124-0_26
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23024-3
Online ISBN: 978-3-540-30124-0
eBook Packages: Springer Book Archive