Abstract
We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form y i#y j + c i,j where y i is either x í or xi, the values of the counter i respectively after and before the transition, and # is any relational symbol in {=,≤,≥,>,<}. We show that the set of possible counter values which can be reached after any number of iterations of a loop is definable in the additive theory of ℕ (or ℤ or ℝ depending on the type of the counters). This result can be used for the safety analysis of multiple counters automata.
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References
R. Alur and D. Dill. Automata for modeling real-time systems. In Proc. 17th Int. Coll. on Automata, Languages and Programming, Warwick, LNCS 443, pages 322–335. Springer-Verlag, 1990.
O. Bernholtz, M. Vardi, and P. Wolper.An automata-theoretic approach to branching time model checking. In Proc. Computer Aided Verification, 1994.
B. Boigelot. Linear operators and regular languages (ii). Unpublished draft, jan 1997.
B. Boigelot and P. Wolper. Symbolic verification with periodic sets. In Computer Aided Verification, Proc. 6th Int. Conerence, LNCS, Stanford, June 1994. Springer-Verlag.
T. Bultan, R. Gerber, and W. Pugh. Symbolic model checking of infinite state systems using presburger arithmetic. In O. Grumberg, editor, Proc. Computer Aided Verification, volume 1254 of LNCS, Haifa, Israel, 1997. Springer-Verlag.
T. Cormen, C. Leiserson, and R. Rivest. Introduction to algorithms. MIT Press, 1990.
P. Cousot and N. Halbwachs. Automatic discovery of linear restraints among variables of a program. In Proc. Int. Conf. on Princinples Of Programming Languages (POPL), 1978.
J. Esparza. Decidabihty of model checking for infinite-state concurrent systems. Acta Informatica, 34:85–107, 1997.
L. Fribourg. A closed form evaluation for extending timed automata. Technical Report 1998-02, Laboratoire Spécification et Vérification, ENS Cachan, Mar. 1998.
L. Fribourg and H. Olsen. A decompositional approach for computing least fixedpoint of datalog programs with z-counters. J. Constraints, 1997.
L. Fribourg and J. Richardson. Symbolic verification with gap-order constraints. Research Report LIENS-96-3, Ecole Normale Supérieure, Paris, Feb. 1996.
N. Halbwachs. Delay analysis in synchronous programs. In Proc. Computer Aided Verification, LNCS 697, pages 333–346. Springer-Verlag, 1993.
M. Minsky. Computation, Finite and Infinite Machines. Prentice Hall, 1967.
R. Parikh. On context-free languages. J. ACM, 13, 1966.
P. Revesz. A closed form for datalog queries with integer order. In Proc 3rd International Conference on Database Theory, pages 187–201, Paris, 1990.
W. Thomas. Automata on infinite objects. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 134–191. Elsevier, 1990.
D. Toman, J. Chomicki, and D. S. Rogers. Datalog with integer periodicity constraints. In Int. Symp. on Logic Programming, 1994.
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Comon, H., Jurski, Y. (1998). Multiple counters automata, safety analysis and presburger arithmetic. In: Hu, A.J., Vardi, M.Y. (eds) Computer Aided Verification. CAV 1998. Lecture Notes in Computer Science, vol 1427. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028751
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DOI: https://doi.org/10.1007/BFb0028751
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