Abstract
The paper presents the method of network invariants for verifying a wide spectrum of LTL properties, including liveness, of parameterized systems. This method can be applied to establish the validity of the property over a system S(n) for every value of the parameter n. The application of the method requires checking abstraction relations between two finite-state systems. We present a proof rule, based on the method of Abstraction Mapping by Abadi and Lamport, which has been implemented on the tlv modelc hecker and incorporates both history and prophecy variables. The effectiveness of the network invariant method is illustrated on several examples, including a deterministic and probabilistic versions of the dining-philosophers problem.
This research was supported in part by the John von Neumann Minerva Center for Verification of Reactive Systems, The European Community IST project “Advance”, and ONR grant N00014-99-1-0131.
This is a preview of subscription content, log in via an institution to check access.
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
M. Abadi and L. Lamport. The existence of refinement mappings. Theoretical Computer Science, 82(2):253–284, May 1991.
K. R. Apt and D. Kozen. Limits for automatic program verification of finite-state concurrent systems. Information Processing Letters, 22(6), 1986.
M. Browne, E. Clarke, and O. Grumberg. Reasoning about networks with many finite state processes. PODC’86, pages 240–248.
E. Clarke, O. Grumberg, and S. Jha. Verifying parametrized networks using abstraction and regular languages. CONCUR’95, pages 395–407.
E. Dijkstra, W. Feijen, and A. van Gasteren. Derivation of a termination detection algorithm for disrtibued computations. Info. Proc. Lett., 16:217–219, 1983.
E. Emerson and V. Kahlon. Reducing model checking of the many to the few. In CADE-17, pages 236–255, 2000.
E. Emerson and K. Namjoshi. Automatic verification of parameterized synchronous systems. CAV’96, LNCS 1102.
N. Halbwachs, F. Lagnier, and C. Ratel. An experience in proving regular networks of processes by modular model checking. Acta Informatica, 29(6/7):523–543, 1992.
C. Ip and D. Dill. Verifying systems with replicated components in Murφ. CAV’96, LNCS 1102.
Y. Kesten and A. Pnueli. Control and data abstractions: The cornerstones of formal verification. Software Tools for Technology Transfer, 2(4):328–342, 2000.
Y. Kesten and A. Pnueli. Verification by augmented finitary abstraction. Information and Computation, a special issue on Compositionality, 163:203–243, 2000.
Y. Kesten, A. Pnueli, E. Shahar, and L. D. Zuck. Network invariant in action. Technical report, The weizmann Institute of Science, 2002.
R. P. Kurshan and K. L. McMillan. A structural induction theorem for processes. Information and Computation, 117:1–11, 1995.
D. Lehmann and M. O. Rabin. On the advantages of free choice: A symmetric and fully distributed solution to the dining philosophers problem. POPL’81, pages 133–138.
D. Lesens, N. Halbwachs, and P. Raymond. Automatic verification of parameterized linear networks of processes. POPL’97.
Z. Manna, A. Anuchitanukul, N. Bjørner, A. Browne, E. Chang, M. Colón, L. D. Alfaro, H. Devarajan, H. Sipma, and T. Uribe. STeP: The Stanford Temporal Prover. Stanford, California, 1994.
Z. Manna and A. Pnueli. The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer Verlag, New York, 1991.
Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, New York, 1995.
A. Pnueli, S. Ruah, and L. Zuck. Automatic deductive verification with invisible invariants. TACAS’01, LNCS 2031, pages 82–97.
A. Pnueli and E. Shahar. A platform for combining deductive with algorithmic verification. CAV’96, LNCS 1102, pages 184–195.
A. Pnueli, J. Xu, and L. Zuck. Liveness with (0, 1,∞)-counter abstraction. To appear in CAV’02.
A. Roychoudhury and I. Ramakrishnan. Automated inductive verification of parameterized protocols. CAV’01, LNCS 2102.
Z. Shtadler and O. Grumberg. Network grammars, communication behaviors and automatic verification. CAV’89, LNCS 407, pages 151–165.
A. Sistla and S. German. Reasoning about systems with many processes. J. ACM, 39:675–735, 1992.
P. Wolper and V. Lovinfosse. Verifying properties of large sets of processes with network invariants. CAV’89, LNCS 407, pages 68–80.
L. Zuck, A. Pnueli, and Y. Kesten. Automatic verification of free choice. In Proc. of the 3rd workshop on Verification, Model Checking, and Abstract Interpretation, LNCS 2294, 2002.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kesten, Y., Pnueli, A., Shahar, E., Zuck, L. (2002). Network Invariants in Action* . In: Brim, L., Křetínský, M., Kučera, A., Jančar, P. (eds) CONCUR 2002 — Concurrency Theory. CONCUR 2002. Lecture Notes in Computer Science, vol 2421. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45694-5_8
Download citation
DOI: https://doi.org/10.1007/3-540-45694-5_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44043-7
Online ISBN: 978-3-540-45694-0
eBook Packages: Springer Book Archive