Parametrized verification of linear networks using automata as invariants
In this paper we proposed a formalism based on automata on two dimensional strings for specifying inductive invariants for proving correctness of families of linear and circular networks. We proved our inductive approach to be sound and complete (semantical completeness). We have illustrated our approach by simple examples.
We have also given the inductive approach for verification of parametrized systems under fairness. In this case, we use generalized Buchi automata (or Streett automata) as inductive invariants. For this case, we have proved the soundness theorem.
As part of future work, it will be interesting to automate the different parts of the induction based approach and apply them to real practical examples. It will also be interesting to extend our approach to networks defined by context free grammars [SG89]. Further more, it will also be interesting to investigate logic based approaches for specification of the invariants.
- [AK86]K. R. Apt and D. Kozen: Limits to Automatic Program Verification. Information Processing Letters, 22.6 (1986), 307–309Google Scholar
- [BCG89]M. Browne, E. M. Clarke and O. Grumberg: Reasoning About Networks with Many Identical Finite State Processes. Inf. and Computation, 81(1):13–31, Apr. 1989.Google Scholar
- [CGJ95]E. M. Clarke, O. Grumberg and S. Jha: Verifying Parametrized Networks Using Abstraction and Regular Languages. CONCUR 95.Google Scholar
- [CG87]E. M. Clarke, and O. Grumberg: Avoiding the State Explosion Problem in Temporal Logic Modelchecking Problem. In Proceedings of ACM Symposium on Principles of Distributed Computing 1987.Google Scholar
- [EN95]E. A. Emerson and K. S. Namjoshi: Reasoning About Rings, Proceedings of 22nd POPL conferece, Jan 1995.Google Scholar
- [EN96]E. A. Emerson and K. S. Namjoshi: Automatic Verification of Parametrized Synchronous Systems. Proceeding of the International Conference on Computer Aide Verification 1996.Google Scholar
- [GS92]S. M. German and A. P. Sistla: Reasoning About Systems with many Processes. JACM, July 1992, Vol 39, No. 3, pp 675–735.Google Scholar
- [GW91]P. Godefroid and P. Wolper: Using Partial Approach to Modelchecking. Proc 6th IEEE Symposium on Logic in Computer Science, pp 406–415, Amsterdam, July 1991.Google Scholar
- [KM89]R. P. Kurshan and K. McMillan: A Structural Induction Theorem for Processes. ACM Sym. on Principles of Distributed Computing, Aug. 1989.Google Scholar
- [SG89]Z. Shtadler and O. Grumberg: Network Grammars, Communication Behaviors and Automatic Verififcation. Proc. of International Workshop on Automatic Verification Methods for Finite State Systems, June 1989.Google Scholar
- [Si97]A. P. Sistla: Parametrized Verification of Linear Networks Using Automata as Invariants. Technical report, University of Illinois at Chicago 1997.Google Scholar
- [SVW85]A. P. Sistla, M. Vardi and P. Wolper: The Complementation Problem for Buchi Automata and Applications to Temporal Logics. Proceedings Of The 12th International Colloquium On Automata, Languages And Programming, Greece, August 1985; The journal version of the paper appeared in Theoretical Computer Science, 49, No 2,3 1987, pp 217–237.Google Scholar
- [SG87]A. P. Sistla and S. M. German: Reasoning About many Processes. LICS 87.Google Scholar
- [WL89]P. Wolper and V. Lovinfosse: Verifying Properties of Large Sets of Processes with Network Invariants. Proc. 1989 Intl Wokshop on Automatic Verification Methods for Finite State Systems 1989.Google Scholar