Abstract
We consider a model for representing infinite-state and parameterized systems, in which states are represented as strings over a finite alphabet. Actions are transformations on strings, in which the change can be characterized by an arbitrary finite-state transducer. This program model is able to represent programs operating on a variety of data structures, such as queues, stacks, integers, and systems with a parameterized linear topology. The main contribution of this paper is an effective derivation of a general and powerful transitive closure operation for this model. The transitive closure of an action represents the effect of executing the action an arbitrary number of times. For example, the transitive closure of an action which transmits a single message to a buffer will be an action which sends an arbitrarily long sequence of messages to the buffer. Using this transitive closure operation, we show how to model and automatically verify safety properties for several types of infinite-state and parameterized systems.
support in part by the ASTEC competence center, and by the Swedish Board for Industrial and Technical Development (NUTEK)
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References
Parosh Aziz Abdulla, Ahmed Bouajjani, and Bengt Jonsson. On-the-fly analysis of systems with unbounded, lossy fifo channels. In Proc. 10th CAV, volume 1427 of LNCS, pages 305–318, 1998. 223
Parosh Aziz Abdulla, Ahmed Bouajjani, Bengt Jonsson, and Marcus Nilsson. Handling global conditions in parameterized system verification. In Proc. 11th CAV, volume 1633 of LNCS, pages 134–145, 1999. 220, 222, 224, 226, 231, 233
R. Alur, C. Courcoubetis, and D. Dill. Model-checking for real-time systems. In Proc. 5th LICS, pages 414–425, Philadelphia, 1990. 220
Parosh Aziz Abdulla, Karlis Čerāns, Bengt Jonsson, and Tsay Yih-Kuen. General decidability theorems for infinite-state systems. In Proc. 11th LICS, pages 313–321, 1996. 222
R. Alur and T. Henzinger. A really temporal logic. In Proc. 30th Annual Symp. Foundations of Computer Science, pages 164–169, 1989. 220
Parosh Aziz Abdulla and Bengt Jonsson. Verifying programs with unreliable channels. Information and Computation, 127(2):91–101, 1996. 220, 222, 232
J.R. Burch, E.M. Clarke, K.L. McMillan, D.L. Dill, and L.J. Hwang. Symbolic model checking: 1020 states and beyond. In Proc. 5th LICS, 1990. 220
B. Boigelot and P. Godefroid. Symbolic verification of communication protocols with infinite state spaces using QDDs. In Alur and Henzinger, editors, Proc. 8th CAV, volume 1102 of Lecture Notes in Computer Science, pages 1–12. Springer Verlag, 1996. 223, 229, 230, 233
B. Boigelot, P. Godefroid, B. Willems, and P. Wolper. The power of QDDs. In Proc. of the Fourth International Static Analysis Symposium, LNCS. Springer Verlag, 1997. 223, 229
A. Bouajjani and P. Habermehl. Symbolic reachability analysis of fifochannel systems with nonregular sets of configurations. In Proc. ICALP’ 97, volume 1256 of Lecture Notes in Computer Science, 1997. 223
R.E. Bryant. Graph-based algorithms for boolean function manipulation. IEEE Trans. on Computers, C-35(8):677–691, Aug. 1986. 231
O. Burkart and B. Steffen. Composition, decomposition, and model checking of pushdown processes. Nordic Journal of Computing, 2(2):89–125, 1995. 220
B. Boigelot and P. Wolper. Symbolic verification with periodic sets. In Proc. 6th CAV, volume 818 of LNCS, pages 55–67. Springer Verlag, 1994. 223
P. Cousot and R. Cousot. Abstract interpretation: A unified model for static analysis of programs by construction or approximation of fixpoints. In Proc. 4th ACM Symp. on Principles of Programming Languages, pages 238–252, 1977. 223
E.W. Dijkstra, W.H.J. Feijen, and A.J.M. van Gasteren. Derivation of a termination detection algorithm for distributed somputations. Information Processing Letters, 16(5):217–219, 1983. 224, 232
A. Finkel. Decidability of the termination problem for completely specified protocols. Distributed Computing, 7(3), 1994. 220
L. Fribourg and H. Olsén. Reachability sets of parametrized rings as regular languages. In Proc. 2nd Int. Workshop on Verification of Infinite State Systems (INFINITY’97), volume 9 of Electronical Notes in Theoretical Computer Science. Elsevier Science Publishers, July 1997. 222
S. M. German and A. P. Sistla. Reasoning about systems with many processes. Journal of the ACM, 39(3):675–735, 1992. 220
J.G. Henriksen, J. Jensen, M. Jørgensen, N. Klarlund, B. Paige, T. Rauhe, and A. Sandholm. Mona: Monadic second-order logic in practice. In Proc. TACAS’ 95, 1th Int. Conf. on Tools and Algorithms for the Construction and Analysis of Systems, volume 1019 of LNCS, 1996. 222
J.G. Henriksen, J. Jensen, M. Jørgensen, N. Klarlund, B. Paige, T. Rauhe, and A. Sandholm. Mona: Monadic second-order logic in practice. In Tools and Algorithms for the Construction and Analysis of Systems, First International Workshop, TACAS’ 95, LNCS 1019, 1996. Also available through http://www.brics.dk/~klarlund/Mona/main.html. 231
N. Klarlund and A. Møller. MONA Version 1.3 User Manual. BRICS Notes Series NS-98-3 (2.revision), Department of Computer Science, University of Aarhus, October 1998. 231
Y. Kesten, O. Maler, M. Marcus, A. Pnueli, and E. Shahar. Symbolic model checking with rich assertional languages. In O. Grumberg, editor, Proc. 9th CAV, volume 1254, pages 424–435, Haifa, Israel, 1997. Springer Verlag. 220, 221, 222, 226
P. Kelb, T. Margaria, M. Mendler, and C. Gsottberger. Mosel: A flexible toolset for monadic second-order logic. In Proc. of the Int. Workshop on Tools and Algorithms for the Construction and Analysis of Systems (TACAS’97), Enschede (NL), volume 1217 of LNCS, pages 183–202, Heidelberg, Germany, March 1997. Springer-Verlag. 222
A. Prasad Sistla. Parametrized verification of linear networks using automata as invariants. In O. Grumberg, editor, Proc. 9th CAV, volume 1254 of LNCS, pages 412–423, Haifa, Israel, 1997. Springer Verlag. 222
C. Stirling. Decidability of bisimulation equivalence for normed pushdown processes. In Proc. CONCUR’ 96, 7th Int. Conf. on Concurrency Theory, volume 1119 of LNCS, pages 217–232. Springer Verlag, 1996. 220
M. Y. Vardi and P. Wolper. An automata-theoretic approach to automatic program verification. In Proc. 1st LICS, pages 332–344, June 1986. 226
Pierre Wolper and Bernard Boigelot. Verifying systems with infinite but regular state spaces. In Proc. 10th CAV, volume 1427 of LNCS, pages 88–97, Vancouver, July 1998. Springer Verlag. 222
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Jonsson, B., Nilsson, M. (2000). Transitive Closures of Regular Relations for Verifying Infinite-State Systems. 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_16
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