Automatic verification of real-time systems with discrete probability distributions

We consider the timed automata model of Alur and Dill (Theoret. Comput. Sci. 126 (1994) 183-235), which allows the analysis of real-time systems expressed in terms of quantitative timing constraints. Traditional approaches to real-time system description express the model purely in terms of nondeterminism; however, it is often desirable to express the likelihood of the system making certain transitions. In this paper, we present a model for real-time systems augmented with discrete probability distributions. Furthermore, two approaches to model checking are introduced for this model. The first uses the algorithm of Baier and Kwiatkowska (Distributed Comput. 11 (1998) 125-155) to provide a verification technique against temporal logic formulae which can refer both to timing properties and probabilities. The second, generally more efficient, technique concerns the verification of probabilistic, real-time reachability properties.

[1]  Stavros Tripakis,et al.  Analysis of Timed Systems Based on Time-Abstracting Bisimulation , 1996, CAV.

[2]  Luca de Alfaro,et al.  Computing Minimum and Maximum Reachability Times in Probabilistic Systems , 1999, CONCUR.

[3]  Satoshi Yamane,et al.  The symbolic model-checking for real-time systems , 1996, Proceedings of the Eighth Euromicro Workshop on Real-Time Systems.

[4]  Stavros Tripakis,et al.  Kronos: A Model-Checking Tool for Real-Time Systems , 1998, CAV.

[5]  Marta Kwiatkowska,et al.  Symbolic Model Checking of Probabilistic Timed Automata Using Backwards Reachability , 2000 .

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

[7]  Nancy A. Lynch,et al.  Probabilistic Simulations for Probabilistic Processes , 1994, Nord. J. Comput..

[8]  Wang Yi,et al.  New Generation of UPPAAL , 1998 .

[9]  George J. Pappas,et al.  Decidable Hybrid Systems , 1998 .

[10]  Wang Yi,et al.  Uppaal in a nutshell , 1997, International Journal on Software Tools for Technology Transfer.

[11]  Rajeev Alur,et al.  Model-Checking for Probabilistic Real Time Systems , 1991 .

[12]  Christel Baier,et al.  Deciding Bisimilarity and Similarity for Probabilistic Processes , 2000, J. Comput. Syst. Sci..

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

[14]  Theo C. Ruys,et al.  The Bounded Retransmission Protocol Must Be on Time! , 1997, TACAS.

[15]  P. Varaiya,et al.  Decidable hybrid systems , 1996 .

[16]  Stavros Tripakis,et al.  Verifying Progress in Timed Systems , 1999, ARTS.

[17]  R. Segala,et al.  Automatic Verification of Real-Time Systems with Discrete Probability Distributions , 1999, ARTS.

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

[19]  Stavros Tripakis,et al.  On-the-fly symbolic model checking for real-time systems , 1997, Proceedings Real-Time Systems Symposium.

[20]  Christel Baier,et al.  On the Verification of Qualitative Properties of Probabilistic Processes under Fairness Constraints , 1998, Inf. Process. Lett..

[21]  Sergio Yovine,et al.  Model Checking Timed Automata , 1996, European Educational Forum: School on Embedded Systems.

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

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

[24]  Christel Baier,et al.  Polynomial Time Algorithms for Testing Probabilistic Bisimulation and Simulation , 1996, CAV.

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

[26]  Rajeev Alur,et al.  Model-Checking for Probabilistic Real-Time Systems (Extended Abstract) , 1991, ICALP.

[27]  Kim G. Larsen,et al.  Bisimulation through Probabilistic Testing , 1991, Inf. Comput..

[28]  Thomas A. Henzinger,et al.  From Quantity to Quality , 1997, HART.

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

[30]  P. R. d' Argenio,et al.  Modelling and Verifying a Bounded Retransmission Protocol , 1996, FME 1996.

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

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

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