Partial Order Methods for Statistical Model Checking and Simulation

Statistical model checking has become a promising technique to circumvent the state space explosion problem in model-based verification. It trades time for memory, via a probabilistic simulation and exploration of the model behaviour--often combined with effective a posteriori hypothesis testing. However, as a simulation-based approach, it can only provide sound verification results if the underlying model is a stochastic process. This drastically limits its applicability in verification, where most models are indeed variations of nondeterministic transition systems. In this paper, we describe a sound extension of statistical model checking to scenarios where nondeterminism is present. We focus on probabilistic automata, and discuss how partial order reduction can be twisted such as to apply statistical model checking to models with spurious nondeterminism. We report on an implementation of this technique and on promising results in the context of verification and dependability analysis of distributed systems.

[1]  Averill M. Law,et al.  Simulation modelling and analysis , 1991 .

[2]  Håkan L. S. Younes,et al.  Probabilistic Verification of Discrete Event Systems Using Acceptance Sampling , 2002, CAV.

[3]  Christel Baier,et al.  Partial Order Reduction for Probabilistic Branching Time , 2006, QAPL.

[4]  Neil D. Lawrence,et al.  Missing Data in Kernel PCA , 2006, ECML.

[5]  David Lee,et al.  Formal Techniques for Distributed Systems, Joint 11th IFIP WG 6.1 International Conference FMOODS 2009 and 29th IFIP WG 6.1 International Conference FORTE 2009, Lisboa, Portugal, June 9-12, 2009. Proceedings , 2009, FMOODS/FORTE.

[6]  Csaba Szepesvári,et al.  Bandit Based Monte-Carlo Planning , 2006, ECML.

[7]  Todd R. Andel,et al.  On the credibility of manet simulations , 2006, Computer.

[8]  Håkan L. S. Younes,et al.  Numerical vs. Statistical Probabilistic Model Checking: An Empirical Study , 2004, TACAS.

[9]  Holger Hermanns,et al.  MODEST: A Compositional Modeling Formalism for Hard and Softly Timed Systems , 2006, IEEE Transactions on Software Engineering.

[10]  Holger Hermanns,et al.  A Modest Approach to Checking Probabilistic Timed Automata , 2009, 2009 Sixth International Conference on the Quantitative Evaluation of Systems.

[11]  Mario Bravetti,et al.  CONCUR 2009 - Concurrency Theory, 20th International Conference, CONCUR 2009, Bologna, Italy, September 1-4, 2009. Proceedings , 2009, CONCUR.

[12]  Christel Baier,et al.  Principles of Model Checking (Representation and Mind Series) , 2008 .

[13]  Doron A. Peled Combining Partial Order Reductions with On-the-fly Model-Checking , 1994, CAV.

[14]  Antti Valmari,et al.  A stubborn attack on state explosion , 1990, Formal Methods Syst. Des..

[15]  Mariëlle Stoelinga,et al.  Alea jacta est : verification of probabilistic, real-time and parametric systems , 2002 .

[16]  Pedro R. D'Argenio,et al.  Partial Order Reduction for Probabilistic Systems: A Revision for Distributed Schedulers , 2009, CONCUR.

[17]  Joost-Pieter Katoen,et al.  Simulation-Based CTMC Model Checking: An Empirical Evaluation , 2009, 2009 Sixth International Conference on the Quantitative Evaluation of Systems.

[18]  Christel Baier,et al.  Principles of model checking , 2008 .

[19]  David Anthony Parker,et al.  Implementation of symbolic model checking for probabilistic systems , 2003 .

[20]  André Schiper,et al.  On the accuracy of MANET simulators , 2002, POMC '02.

[21]  Axel Legay,et al.  Statistical Abstraction and Model-Checking of Large Heterogeneous Systems , 2010 .

[22]  C. A. Petri,et al.  Concurrency Theory , 1986, Advances in Petri Nets.

[23]  Matthias Kuntz,et al.  Architectural dependability evaluation with Arcade , 2008, 2008 IEEE International Conference on Dependable Systems and Networks With FTCS and DCC (DSN).

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

[25]  Marius Minea,et al.  Partial Order Reduction for Model Checking of Timed Automata , 1999, CONCUR.

[26]  Joost-Pieter Katoen,et al.  A Linear Process-Algebraic Format for Probabilistic Systems with Data , 2010, 2010 10th International Conference on Application of Concurrency to System Design.

[27]  Roberto Segala,et al.  Modeling and verification of randomized distributed real-time systems , 1996 .

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

[29]  Patrice Godefroid,et al.  Partial-Order Methods for the Verification of Concurrent Systems , 1996, Lecture Notes in Computer Science.

[30]  Edmund M. Clarke,et al.  Bayesian statistical model checking with application to Stateflow/Simulink verification , 2010, Formal Methods in System Design.