INFAMY: An Infinite-State Markov Model Checker

The design of complex concurrent systems often involves intricate performance and dependability considerations. Continuous-time Markov chains (CTMCs) are a widely used modeling formalism, where performance and dependability properties are analyzable by model checking. We present INFAMY , a model checker for arbitrarily structured infinite-state CTMCs. It checks probabilistic timing properties expressible in continuous stochastic logic (CSL). Conventional model checkers explore the given model exhaustively, which is often costly, due to state explosion, and impossible if the model is infinite. INFAMY only explores the model up to a finite depth, with the depth bound being computed on-the-fly . The computation of depth bounds is configurable to adapt to the characteristics of different classes of models.

[1]  Peter W. Glynn,et al.  Computing Poisson probabilities , 1988, CACM.

[2]  W. Sanders.  Adaptive Uniformization , 1994 .

[3]  Gerard J. Holzmann,et al.  The Model Checker SPIN , 1997, IEEE Trans. Software Eng..

[4]  P J Goss,et al.  Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[5]  M. Siegle,et al.  Multi Terminal Binary Decision Diagrams to Represent and Analyse Continuous Time Markov Chains , 1999 .

[6]  Joost-Pieter Katoen,et al.  On the use of model checking techniques for dependability evaluation , 2000, Proceedings 19th IEEE Symposium on Reliable Distributed Systems SRDS-2000.

[7]  Robert K. Brayton,et al.  Model-checking continuous-time Markov chains , 2000, TOCL.

[8]  Thomas Hérault,et al.  Approximate Probabilistic Model Checking , 2004, VMCAI.

[9]  Kousha Etessami,et al.  Analysis of Recursive Game Graphs Using Data Flow Equations , 2004, VMCAI.

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

[11]  Håkan L. S. Younes.  Ymer: A Statistical Model Checker , 2005, CAV.

[12]  Christel Baier,et al.  Model checking meets performance evaluation , 2005, PERV.

[13]  M. Khammash,et al.  The finite state projection algorithm for the solution of the chemical master equation. , 2006, The Journal of chemical physics.

[14]  Andrew Hinton,et al.  PRISM: A Tool for Automatic Verification of Probabilistic Systems , 2006, TACAS.

[15]  Joost-Pieter Katoen,et al.  Three-Valued Abstraction for Continuous-Time Markov Chains , 2007, CAV.

[16]  Lijun Zhang,et al.  Time-bounded model checking of infinite-state continuous-time Markov chains , 2008, 2008 8th International Conference on Application of Concurrency to System Design.

[17]  Ivan S. Zapreev.  Model checking Markov chains : techniques and tools , 2008 .