Abstract
We present a method that allows to verify parameterized networks of finite state processes. Our method is based on three main ideas. The first one consists in modeling an infinite family of networks by a single WS1S transition system, that is, a transition system whose variables are set (2nd-order) variables and whose transitions are described in WS1S. Then, we present methods that allow to abstract a WS1S system into a finite state system that can be model-checked. Finally, in order to verify liveness properties, we present an algorithm that allows to enrich the abstract system with strong fairness conditions while preserving safety of the abstraction. We implemented our method in a tool, called pax, and applied it to several examples.
This work has been partially supported by the Esprit-LTR project Vires.
Contact Author.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
P.A. Abdulla, A. Bouajjani, B. Jonsson, and M. Nilsson. Handling Global Conditions in Parameterized System Verification. In N. Halbwachs and D. Peled, editors, CAV’ 99, volume 1633 of LNCS, pages 134–145. Springer, 1999. 189, 191, 202
K. Apt and D. Kozen. Limits for Automatic Verification of Finit-State Concurrent Systems. Information Processing Letters, 22(6):307–309, 1986. 188
M.C. Browne, E.M. Clarke, and O. Grumberg. Reasoning about networks with many identical finite state processes. Information and Computation, 1989. 188
J.R. Büchi. Weak Second-Order Arithmetic and Finite Automata. Z. Math. Logik Grundl. Math., 6:66–92, 1960. 190
E. Clarke, O. Grumberg, and S. Jha. Verifying Parameterized Networks using Abstraction and Regular Languages. In I. Lee and S. Smolka, editors, CONCUR’ 95: Concurrency Theory, LNCS. Springer, 1995. 188
E. M. Clarke, O. Grumberg, and D. E. Long. Model checking and abstraction. ACM Transactions on Programming Languages and Systems, 16(5), 1994. 189, 195
D. Dams, R. Gerth, and O. Grumberg. Abstract interpretation of reactive systems: Abstractions preserving ACTL*, ECTL* and CTL*. In E.-R. Olderog, editor, Proceedings of PROCOMET’ 94. North-Holland, 1994. 189, 195
C.C. Elgot. Decision problems of finite automata design and related arithmetics. Trans. Amer. Math. Soc., 98:21–52, 1961. 190
E. A. Emerson and K. S. Namjoshi. Reasoning about rings. In 22nd ACM Symposium on Principles of Programming Languages, pages 85–94, 1995. 188
E. A. Emerson and K. S. Namjoshi. Automatic verification of parameterized synchronous systems. In 8th Conference on Computer Aided Verification, LNCS 1102, pages 87–98, 1996. 188
O. Grumberg, editor. Proceedings of CAV’ 97, volume 1256 of LNCS. Springer, 1997. 203
S.M. German and A.P. Sistla. Reasoning about systems with many processes. Journal of the ACM, 39(3):675–735, 1992. 188
S. Graf and H. Saidi. Construction of Abstract State Graphs with PVS. In Grumberg [Gru97]. 194
HJJ+96._J.G. Henriksen, J. Jensen, M. Jørgensen, N. Klarlund, B. Paige, T. Rauhe, and A. Sandholm. Mona: Monadic Second-Order Logic in Practice. In TACAS’ 95, volume 1019 of LNCS. Springer, 1996. 190, 194, 198
N. Halbwachs, F. Lagnier, and C. Ratel. An experience in proving regular networks of processes by modular model checking. Acta Informatica, 22(6/7), 1992. 188
R.P. Kurshan and K. McMillan. A structural induction theorem for processes. In ACM Symp. on Principles of Distributed Computing, Canada, pages 239–247, Edmonton, Alberta, 1989. 188
N. Klarlund and A. Møller. MONA Version 1.3 User Manual. BRICS, 1998. 190, 194, 198
KMM+97._Y. Kesten, O. Maler, M. Marcus, A. Pnueli, and E. Shahar. Symbolic Model Checking with Rich Assertional Languages. In Grumberg [Gru97], pages 424–435. 189
LGS+95._C. Loiseaux, S. Graf, J. Sifakis, A. Bouajjani, and S. Bensalem. Property preserving abstractions for the verification of concurrent systems. Formal Methods in System Design, 6(1), 1995. 189, 195
D. Lesens, N. Halbwachs, and P. Raymond. Automatic verification of parameterized linear networks of processes. In POPL’ 97, Paris, 1997. 188
Z. Manna and A. Pnueli. Verification of parameterized programs. In E. Borger, editor, Specification and Validation Methods, pages 167–230, Oxford University Press, 1994. 189
Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems, Safety. Springer Verlag, 1995. 191
Z. Stadler and O. Grumberg. Network grammars, communication behaviours and automatic verification. In Proc. Workshop on Automatic Verification Methods for Finite State Systems, Lecture Notes in Computer Science, pages 151–165, Grenoble, France, 1989. Springer Verlag. 188
B.K. Szymanski. A simple solution to Lamport’s concurrent programming problem with linear wait. In Proceedings of International Conference on Supercomputing Systems 1988, pages 621–626, St. Malo, France, July 1988. 191
W. Thomas. Automata on infinite objects. In Handbook of Theoretical Computer Science, Volume B: Formal Methods and Semantics, pages 134–191. Elsevier Science Publishers B. V., 1990. 190
P. Wolper and V. Lovinfosse. Verifying properties of large sets of processes with network invariants (extended abstract). In Sifakis, editor, Workshop on Computer Aided Verification, LNCS 407, pages 68–80, 1989. 188
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Baukus, K., Bensalem, S., Lakhnech, Y., Stahl, K. (2000). Abstracting WS1S Systems to Verify Parameterized Networks. In: Graf, S., Schwartzbach, M. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2000. Lecture Notes in Computer Science, vol 1785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46419-0_14
Download citation
DOI: https://doi.org/10.1007/3-540-46419-0_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67282-1
Online ISBN: 978-3-540-46419-8
eBook Packages: Springer Book Archive