Model-Checking for Weighted Timed Automata

We study the model-checking problem for weighted timed automata and the weighted CTL logic by the bisimulation approach. Weighted timed automata are timed automata extended with costs on both edges and locations. When the costs act as stopwatches, we get stopwatch automata with the restriction that the stopwatches cannot be reset nor tested. The weighted CTL logic is an extension of TCTL that allow to reset and test the cost variables. Our main results are (i) the undecidability of the proposed model-checking problem for discrete and dense time, (ii) its PSpace-Completeness in the discrete case for a slight restriction of the logic, (iii) the precise frontier between finite and infinite bisimulations in the dense case for the subclass of stopwatch automata.

[1]  Rajeev Alur,et al.  A Temporal Logic of Nested Calls and Returns , 2004, TACAS.

[2]  George J. Pappas,et al.  Discrete abstractions of hybrid systems , 2000, Proceedings of the IEEE.

[3]  Jaikumar Radhakrishnan,et al.  FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science , 2004, Lecture Notes in Computer Science.

[4]  Thomas A. Henzinger,et al.  Automatic symbolic verification of embedded systems , 1993, 1993 Proceedings Real-Time Systems Symposium.

[5]  Thomas A. Henzinger,et al.  Computing Accumulated Delays in Real-time Systems , 1993, Formal Methods Syst. Des..

[6]  Thomas A. Henzinger,et al.  Discrete-Time Control for Rectangular Hybrid Automata , 1997, Theor. Comput. Sci..

[7]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[8]  Thomas A. Henzinger,et al.  A User Guide to HyTech , 1995, TACAS.

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

[10]  George J. Pappas,et al.  Optimal Paths in Weighted Timed Automata , 2001, HSCC.

[11]  Kim G. Larsen,et al.  Minimum-Cost Reachability for Priced Timed Automata , 2001, HSCC.

[12]  Rajeev Alur,et al.  Model-Checking in Dense Real-time , 1993, Inf. Comput..

[13]  Joseph Sifakis,et al.  Decidable Integration Graphs , 1999, Inf. Comput..

[14]  Véronique Bruyère,et al.  Real-Time Model-Checking: Parameters everywhere , 2003, Log. Methods Comput. Sci..

[15]  Thomas A. Henzinger,et al.  Hybrid Systems: Computation and Control , 1998, Lecture Notes in Computer Science.

[16]  Thomas A. Henzinger,et al.  The theory of hybrid automata , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[17]  Thomas A. Henzinger,et al.  Hybrid Automata with Finite Bisimulatioins , 1995, ICALP.

[18]  Pravin Varaiya,et al.  What's decidable about hybrid automata? , 1995, STOC '95.

[19]  Joseph Sifakis,et al.  On model checking for real-time properties with durations , 1993, [1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science.