Better Abstractions for Timed Automata

We consider the reachability problem for timed automata. A standard solution to this problem involves computing a search tree whose nodes are abstractions of zones. These abstractions preserve underlying simulation relations on the state space of the automaton. For both effectiveness and efficiency reasons, they are parameterized by the maximal lower and upper bounds (LU-bounds) occurring in the guards of the automaton. We consider the aLU abstraction defined by Behrmann et al. Since this abstraction can potentially yield non-convex sets, it has not been used in implementations. We prove that aLU abstraction is the coarsest abstraction with respect to LU-bounds that is sound and complete for reachability. We also provide an efficient technique to use the aLU abstraction to solve the reachability problem.

[1]  Robert K. Brayton,et al.  Verifying Abstractions of Timed Systems , 1996, CONCUR.

[2]  Anna Philippou,et al.  Tools and Algorithms for the Construction and Analysis of Systems , 2018, Lecture Notes in Computer Science.

[3]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[4]  Robert E. Shostak,et al.  Deciding Linear Inequalities by Computing Loop Residues , 1981, JACM.

[5]  Patricia Bouyer,et al.  Forward Analysis of Updatable Timed Automata , 2004, Formal Methods Syst. Des..

[6]  David L. Dill,et al.  Timing Assumptions and Verification of Finite-State Concurrent Systems , 1989, Automatic Verification Methods for Finite State Systems.

[7]  Christoph Scholl,et al.  Fully Symbolic Model Checking for Timed Automata , 2011, MBMV.

[8]  Wang Yi,et al.  Timed Automata: Semantics, Algorithms and Tools , 2003, Lectures on Concurrency and Petri Nets.

[9]  Stavros Tripakis,et al.  Analysis of Timed Systems Using Time-Abstracting Bisimulations , 2001, Formal Methods Syst. Des..

[10]  Stavros Tripakis,et al.  Model Checking of Real-Time Reachability Properties Using Abstractions , 1998, TACAS.

[11]  Wang Yi,et al.  UPPAAL 4.0 , 2006, Third International Conference on the Quantitative Evaluation of Systems - (QEST'06).

[12]  Farn Wang,et al.  Efficient verification of timed automata with BDD-like data structures , 2004, International Journal on Software Tools for Technology Transfer.

[13]  Joost-Pieter Katoen,et al.  Time-Abstracting Bisimulation for Probabilistic Timed Automata , 2008, 2008 2nd IFIP/IEEE International Symposium on Theoretical Aspects of Software Engineering.

[14]  Marta Z. Kwiatkowska,et al.  PRISM 4.0: Verification of Probabilistic Real-Time Systems , 2011, CAV.

[15]  Igor Walukiewicz,et al.  Using non-convex approximations for efficient analysis of timed automata , 2011, FSTTCS.

[16]  Igor Walukiewicz,et al.  Lazy abstractions for timed automata , 2013, CAV.

[17]  Kim G. Larsen,et al.  Static Guard Analysis in Timed Automata Verification , 2003, TACAS.

[18]  Mihalis Yannakakis,et al.  Minimum and maximum delay problems in real-time systems , 1991, Formal Methods Syst. Des..

[19]  Bernard Berthomieu,et al.  An Enumerative Approach for Analyzing Time Petri Nets , 1983, IFIP Congress.

[20]  Marta Z. Kwiatkowska,et al.  Automatic verification of real-time systems with discrete probability distributions , 1999, Theor. Comput. Sci..

[21]  Patricia Bouyer,et al.  From Qualitative to Quantitative Analysis of Timed Systems , 2009 .

[22]  David Lee,et al.  An Efficient Algorithm for Minimizing Real-Time Transition Systems , 1997, Formal Methods Syst. Des..

[23]  Philippe Schnoebelen,et al.  The State Explosion Problem from Trace to Bisimulation Equivalence , 2000, FoSSaCS.

[24]  Rajeev Alur,et al.  Minimization of Timed Transition Systems , 1992, CONCUR.

[25]  Kim G. Larsen,et al.  Quantitative analysis of real-time systems using priced timed automata , 2011, Commun. ACM.

[26]  Guoliang Zheng,et al.  A quadratic-time DBM-based successor algorithm for checking timed automata , 2005, Inf. Process. Lett..

[27]  Kim G. Larsen,et al.  Lower and upper bounds in zone-based abstractions of timed automata , 2004, International Journal on Software Tools for Technology Transfer.