Symbolic model checking for probabilistic timed automata

Probabilistic timed automata are an extension of timed automata with discrete probability distributions, and can be used to model timed randomized protocols or fault-tolerant systems. We present symbolic model-checking algorithms for verifying probabilistic timed automata against properties of PTCTL (Probabilistic Timed Computation Tree Logic). The algorithms operate on zones, which are sets of valuations of the probabilistic timed automaton's clocks, and therefore avoid an explicit construction of the state space. Furthermore, the algorithms are restricted to system behaviours which guarantee the divergence of time with probability 1. We report on a prototype implementation of the algorithms using Difference Bound Matrices, and present the results of its application to the CSMA/CD and FireWire root contention protocol case studies.

[1]  Stavros Tripakis,et al.  L'analyse formelle des systèmes temporisés en pratique. (The Formal Analysis of Timed Systems in Practice) , 1998 .

[2]  Farn Wang,et al.  TCTL Inevitability Analysis of Dense-Time Systems , 2003, CIAA.

[3]  Zohar Manna,et al.  Formal verification of probabilistic systems , 1997 .

[4]  Marta Z. Kwiatkowska,et al.  PRISM: Probabilistic Symbolic Model Checker , 2002, Computer Performance Evaluation / TOOLS.

[5]  R. BurchJ.,et al.  Symbolic model checking , 1992 .

[6]  Christel Baier,et al.  Model checking for a probabilistic branching time logic with fairness , 1998, Distributed Computing.

[7]  Edmund M. Clarke,et al.  Symbolic Model Checking: 10^20 States and Beyond , 1990, Inf. Comput..

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

[9]  S. Hart,et al.  Termination of Probabilistic Concurrent Programs. , 1982 .

[10]  Edmund M. Clarke.  Automatic verification of finite-state concurrent systems , 1994, Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science.

[11]  Mariëlle Stoelinga,et al.  Mechanical verification of the IEEE 1394a root contention protocol using Uppaal2k , 2001, International Journal on Software Tools for Technology Transfer.

[12]  Marta Z. Kwiatkowska,et al.  Probabilistic Model Checking of Deadline Properties in the IEEE 1394 FireWire Root Contention Protocol , 2003, Formal Aspects of Computing.

[13]  Conrado Daws,et al.  Automatic verification of the IEEE 1394 root contention protocol with KRONOS and PRISM , 2002, International Journal on Software Tools for Technology Transfer.

[14]  N. S. Barnett,et al.  Private communication , 1969 .

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

[16]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[17]  Marta Z. Kwiatkowska,et al.  Probabilistic Model Checking of the IEEE 802.11 Wireless Local Area Network Protocol , 2002, PAPM-PROBMIV.

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

[19]  Joseph Sifakis,et al.  Compiling Real-Time Specifications into Extended Automata , 1992, IEEE Trans. Software Eng..

[20]  Amir Pnueli,et al.  On the extremely fair treatment of probabilistic algorithms , 1983, STOC.

[21]  Micha Sharir,et al.  Termination of Probabilistic Concurrent Program , 1983, TOPL.

[22]  Sergio Yovine.  Méthodes et outils pour la vérification symbolique de systèmes temporisés , 1993 .

[23]  J. Kemeny,et al.  Denumerable Markov chains , 1969 .

[24]  Wang Yi,et al.  UPPAAL - present and future , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[25]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[26]  Henrik Ejersbo Jensen.  Model Checking Probabilistic Real Time Systems , 1996 .

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

[28]  Andrea Bianco,et al.  Model Checking of Probabalistic and Nondeterministic Systems , 1995, FSTTCS.

[29]  Marta Z. Kwiatkowska,et al.  Performance analysis of probabilistic timed automata using digital clocks , 2003, Formal Methods Syst. Des..

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

[31]  Luca de Alfaro,et al.  Quantitative Verification and Control via the Mu-Calculus , 2003, CONCUR.

[32]  R. Lathe.  Phd by thesis , 1988, Nature.

[33]  Thomas A. Henzinger,et al.  A classification of symbolic transition systems , 2000, TOCL.

[34]  Alfredo Olivero.  Modélisation et analyse de systèmes temporisés et hybrides , 1994 .

[35]  Marta Z. Kwiatkowska,et al.  Symbolic Computation of Maximal Probabilistic Reachability , 2001, CONCUR.

[36]  Zohar Manna,et al.  The Temporal Logic of Reactive and Concurrent Systems , 1991, Springer New York.

[37]  Danièle Beauquier.  On probabilistic timed automata , 2003, Theor. Comput. Sci..

[38]  Cyrus Derman,et al.  Finite State Markovian Decision Processes , 1970 .

[39]  Thomas A. Henzinger,et al.  Symbolic Model Checking for Real-Time Systems , 1994, Inf. Comput..

[40]  J. Davenport.  Editor , 1960 .

[41]  Stavros Tripakis,et al.  The Tool KRONOS , 1996, Hybrid Systems.

[42]  Bengt Jonsson,et al.  A logic for reasoning about time and reliability , 1990, Formal Aspects of Computing.