Robust Weighted Timed Automata and Games

Weighted timed automata extend timed automata with cost variables that can be used to model the evolution of various quantities. Although cost-optimal reachability is decidable (in polynomial space) on this model, it becomes undecidable on weighted timed games. This paper studies cost-optimal reachability problems on weighted timed automata and games under robust semantics. More precisely, we consider two perturbation game semantics that introduce imprecisions in the standard semantics, and bring robustness properties w.r.t. timing imprecisions to controllers. We give a polynomial-space algorithm for weighted timed automata, and prove the undecidability of cost-optimal reachability on weighted timed games, showing that the problem is robustly undecidable.

[1]  Oded Maler,et al.  Hybrid and Real-Time Systems , 1997 .

[2]  Martin Fränzle,et al.  Analysis of Hybrid Systems: An Ounce of Realism Can Save an Infinity of States , 1999, CSL.

[3]  A. Pnueli,et al.  CONTROLLER SYNTHESIS FOR TIMED AUTOMATA , 2006 .

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

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

[6]  Rajeev Alur,et al.  Perturbed Timed Automata , 2005, HSCC.

[7]  Anuj Puri.  Dynamical Properties of Timed Automata , 2000, Discret. Event Dyn. Syst..

[8]  Ahmed Bouajjani,et al.  Perturbed Turing machines and hybrid systems , 2001, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science.

[9]  Véronique Bruyère,et al.  On the optimal reachability problem of weighted timed automata , 2007, Formal Methods Syst. Des..

[10]  Jirí Srba,et al.  Comparing the Expressiveness of Timed Automata and Timed Extensions of Petri Nets , 2008, FORMATS.

[11]  RaskinJean-François,et al.  On the optimal reachability problem of weighted timed automata , 2007 .

[12]  Thomas A. Henzinger,et al.  Robust Timed Automata , 1997, HART.

[13]  Krishnendu Chatterjee,et al.  Timed Parity Games: Complexity and Robustness , 2008, FORMATS.

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

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

[16]  Alex K. Simpson,et al.  Computational Adequacy in an Elementary Topos , 1998, CSL.

[17]  Jean-François Raskin,et al.  Almost ASAP semantics: from timed models to timed implementations , 2004, Formal Aspects of Computing.

[18]  Joseph Sifakis,et al.  Controller Synthesis for Timed Automata 1 , 1998 .

[19]  Ming-Deh A. Huang,et al.  Proof of proposition 1 , 1992 .

[20]  Patricia Bouyer,et al.  Improved undecidability results on weighted timed automata , 2006, Inf. Process. Lett..

[21]  Thomas A. Henzinger,et al.  Robust Undecidability of Timed and Hybrid Systems , 2000, HSCC.

[22]  Véronique Bruyère,et al.  On Optimal Timed Strategies , 2005, FORMATS.

[23]  Rajeev Alur,et al.  Optimal Reachability for Weighted Timed Games , 2004, ICALP.

[24]  Kousha Etessami,et al.  Verifying Probabilistic Procedural Programs , 2004, FSTTCS.

[25]  Nicolas Markey,et al.  Robust safety of timed automata , 2008, Formal Methods Syst. Des..

[26]  Patricia Bouyer,et al.  Shrinking Timed Automata , 2014, FSTTCS.

[27]  Patricia Bouyer,et al.  Robust Controller Synthesis in Timed Automata , 2013, CONCUR.

[28]  Krishnendu Chatterjee,et al.  Strategy logic , 2007, Inf. Comput..

[29]  Patricia Bouyer,et al.  Robust Reachability in Timed Automata: A Game-Based Approach , 2012, ICALP.

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