Abstract
We propose a new infinite-state model, called the Multi-queue Discrete Timed Automaton MQDTA, which extends Timed Automata with queues, but only has integer-valued clocks. Due to careful restrictions on queue usage, the binary reachability (the set of all pairs of configurations (α, β) of an MQDTA such that α can reach β through zero or more transitions) is effectively semilinear. We then prove the decidability of a class of Presburger formulae defined over the binary reachability, allowing the automatic verification of many interesting properties of a MQDTA. The MQDTA model can be used to specify and verify various systems with unbounded queues, such as a real-time scheduler.
Supported in part by MIUR grants FIRB RBAU01MCAC and COFIN 2001015271.
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References
P. Abdulla and B. Jonsson. Model checking of systems with many identical timed processes. Theoretical Computer Science, 290(1):241–264, 2002.
P. Abdulla and A. Nylén. Timed petri nets and bqos. In ICATPN’2001, 22nd Int. Conf. on application and theory of Petri nets, 2001.
R. Alur, C. Courcoubetis, and D. Dill. Model-checking in dense real-time. Information and Computation, 104(1):2–34, May 1993.
R. Alur and D. L. Dill. A theory of timed automata. Theoretical Computer Science, 126(2):183–235, April 1994.
M. Benedikt P. Godefroid and T. Reps. Model checking of unrestricted hierarchical state machines. In ICALP 2001, of LNCS 2076, pp. 652–666. Springer, 2001.
L. Breveglieri, A. Cherubini, C. Citrini, and S. Crespi Reghizzi. Multiple pushdown languages and grammars. Int. Journal of Found. of Computer Science, 7:253–291, 1996.
L. Breveglieri, A. Cherubini, and S. Crespi Reghizzi. Real-time scheduling by queue automata. In FTRTFT’92, vol/ 571 of LNCS, pages 131–148. Springer, 1992.
L. Breveglieri, A. Cherubini, and S. Crespi Reghizzi. Modelling operating systems schedulers with multi-stack-queue grammars. In Fundamentals of Computation Theory, volume 1684 of LNCS, pages 161–172. Springer, 1999.
G. Cece and A. Finkel. Programs with quasi-stable channels are effectively recognizable. In CAV’97, volume 1254 of LNCS, pages 304–315. Springer, 1997.
H. Comon and Y. Jurski. Multiple counters automata, safety analysis and Presburger arithmetic. In CAV’98, volume 1427 of LNCS, pages 268–279. Springer, 1998.
H. Comon and Y. Jurski. Timed automata and the theory of real numbers. In CONCUR’99, volume 1664 of LNCS, pages 242–257. Springer, 1999.
Zhe Dang. Binary reachability analysis of pushdown timed automata with dense clocks. In CAV’01, volume 2102 of LNCS, pages 506–517. Springer, 2001.
Zhe Dang, O. H. Ibarra, T. Bultan, R. A. Kemmerer, and J. Su. Binary reachability analysis of discrete pushdown timed automata. In CAV’00, LNCS 1855, pages 69–84. Springer, 2000.
S. Ginsburg and E. Spanier. Semigroups, presburger formulas, and languages. Pacific J. of Mathematics, 16:285–296, 1966.
P. Godefroid and R. Jagadeesan. Automatic abstraction using generalized model checking. In CAV’02, volume 2404 of LNCS, pages 137–150. Springer, 2002.
B. Grahlmann. The state of pep. In AMAST’98, LNCS 1548, pages 522–526. Springer, 1998.
T. A. Henzinger, X. Nicollin, J. Sifakis, and S. Yovine. Symbolic model checking for real-time systems. Information and Computation, 111(2):193–244, June 1994.
R. Parikh. On context-free languages. Journal of the ACM, 13:570–581, 1966.
A. Pnueli and E. Shahar. Livenss and acceleraiton in parameterized verification. In CAV’00, volume 1855 of LNCS. Springer, 2000.
W. Pugh. The omega test: a fast and practical integer programming algorithm for dependence analysis. Communications of the ACM, 35(8):102–114, 1992.
B. Steffen and O. Burkart. Model checking the full modal mu-calculus for infinite sequential processes. In ICALP’97, volume 1256 of LNCS, pages 419–429.
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San Pietro, P., Dang, Z. (2003). Automatic Verification of Multi-queue Discrete Timed Automata. In: Warnow, T., Zhu, B. (eds) Computing and Combinatorics. COCOON 2003. Lecture Notes in Computer Science, vol 2697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45071-8_18
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DOI: https://doi.org/10.1007/3-540-45071-8_18
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