Abstract
We discuss the verification of timed systems within predicate logics with explicit time and arithmetical operations. The main problem is to find efficient algorithms to treat practical problems. One way is to find practically decidable classes that englobe this or that class of practical problems. This is our main goal, where we concentrate on one approach that permits to arrive at a kind of small model property. We will also touch the question of extension of these results to probabilistic systems that will be presented in more detail elsewhere.
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References
Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)
Beauquier, D., Crolard, T., Prokofieva, E.: Automatic verification of real time systems: A case study. In: Third Workshop on Automated Verification of Critical Systems (AVoCS 2003), University of Southampton, pp. 98–108 (2003)
Beauquier, D., Crolard, T., Prokofieva, E.: Automatic parametric verification of a root contention protocol based on abstract state machines and first order timed logic. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 372–387. Springer, Heidelberg (2004)
Beauquier, D., Crolard, T., Slissenko, A.: A predicate logic framework for mechanical verification of real-time Gurevich Abstract State Machines: A case study with PVS. Technical Report 00–25, University Paris 12, Department of Informatics (2000), Available at http://www.univ-paris12.fr/lacl/
Beauquier, D., Rabinovich, A., Slissenko, A.: A logic of probability with decidable model-checking. Journal of Logic and Computation, 24 pages (to appear)
Beauquier, D., Slissenko, A.: Periodicity based decidable classes in a first order timed logic. Annals of Pure and Applied Logic, 38 pages (to appear)
Beauquier, D., Slissenko, A.: Decidable verification for reducible timed automata specified in a first order logic with time. Theoretical Computer Science 275(1-2), 347–388 (2002)
Beauquier, D., Slissenko, A.: A first order logic for specification of timed algorithms: Basic properties and a decidable class. Annals of Pure and Applied Logic 113(1-3), 13–52 (2002)
Boigelot, B., Wolper, P.: Representing arithmetic constraints with finite automata: An overview. In: Stuckey, P.J. (ed.) ICLP 2002. LNCS, vol. 2401, pp. 1–19. Springer, Heidelberg (2002)
Clarke, E., Kroening, D., Ouaknine, J., Strichman, O.: Completeness and complexity of bounded model checking. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 85–96. Springer, Heidelberg (2004)
Fagin, R., Halpern, J.: Reasoning about knowledge and probability. J. of the Assoc. Comput. Mach. 41(2), 340–367 (1994)
Gurevich, Y., Huggins, J.: The railroad crossing problem: an experiment with instantaneous actions and immediate reactions. In: Kleine Büning, H. (ed.) CSL 1995. LNCS, vol. 1092, pp. 266–290. Springer, Heidelberg (1996)
Halpern, J.: Presburger arithmetic with unary predicates is π1 1-complete. J. of symbolic Logic 56, 637–642 (1991)
Sanders, J., Curran, E.: Software Quality. Addison-Wesley, Reading (1994)
Slissenko, A.: A logic framework for verification of timed algorithms. Fundamenta Informaticae 69, 1–39 (2004)
Sommerville, I.: Software Engineering, 4th edn. Addison-Wesley, Reading (1992)
Sorea, M.: Bounded model checking for timed automata. Electronic Notes in Theoretical Computer Science 68(5) (2002), http://www.elsevier.com/locate/entcs/volume68.html
Tel, G. (ed.): Introduction to Distributed Algorithms. Cambridge University Press, Cambridge (1994)
Weispfenning, V.: Mixed real-integer linear quantifier elimination. In: Proc. of the 1999 Int. Symp. on Symbolic and Algebraic Computations (ISSAC 1999), pp. 129–136. ACM Press, New York (1999)
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Slissenko, A. (2005). Verification in Predicate Logic with Time: Algorithmic Questions. In: Ong, L. (eds) Computer Science Logic. CSL 2005. Lecture Notes in Computer Science, vol 3634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538363_2
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DOI: https://doi.org/10.1007/11538363_2
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