The Ins and Outs of the Probabilistic Model Checker MRMC

The Markov Reward Model Checker (MRMC) is a software toolfor verifying properties over probabilistic models. It supports PCTL and CSL model checking, and their rewardextensions. Distinguishing features of MRMC are its support for computing time- and reward-bounded reachability probabilities, (property-driven) bisimulation minimization, and precise on-the-fly steady-state detection. Recent tool features include time-bounded reachability analysis for uniform CTMDPs and CSL model checking by discrete-event simulation. This paper presents the tool's current status and its implementation details.

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

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

[3]  Joost-Pieter Katoen,et al.  Discrete-Time Rewards Model-Checked , 2003, FORMATS.

[4]  Joost-Pieter Katoen,et al.  A Markov reward model checker , 2005, Second International Conference on the Quantitative Evaluation of Systems (QEST'05).

[5]  Enrico Tronci,et al.  Finite Horizon Analysis of Markov Chains with the Mur-phi Verifier , 2003, CHARME.

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

[7]  Anna Philippou,et al.  Tools and Algorithms for the Construction and Analysis of Systems , 2018, Lecture Notes in Computer Science.

[8]  J. Ian Munro,et al.  Sorting and Searching in Multisets , 1976, SIAM J. Comput..

[9]  Antti Valmari,et al.  Efficient Minimization of DFAs with Partial Transition Functions , 2008, STACS.

[10]  Mahesh Viswanathan,et al.  On Statistical Model Checking of Stochastic Systems , 2005, CAV.

[11]  Christel Baier,et al.  LiQuor: A tool for Qualitative and Quantitative Linear Time analysis of Reactive Systems , 2006, Third International Conference on the Quantitative Evaluation of Systems - (QEST'06).

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

[13]  Susanna Donatelli,et al.  CSL Model Checking for the GreatSPN Tool , 2004, ISCIS.

[14]  Diego Latella,et al.  Model checking dependability attributes of wireless group communication , 2004, International Conference on Dependable Systems and Networks, 2004.

[15]  Joost-Pieter Katoen,et al.  The COMPASS Approach: Correctness, Modelling and Performability of Aerospace Systems , 2009, SAFECOMP.

[16]  Greg N. Frederickson,et al.  Sequencing Tasks with Exponential Service Times to Minimize the Expected Flow Time or Makespan , 1981, JACM.

[17]  William J. Stewart,et al.  Introduction to the numerical solution of Markov Chains , 1994 .

[18]  Håkan L. S. Younes,et al.  Numerical vs. statistical probabilistic model checking , 2006, International Journal on Software Tools for Technology Transfer.

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

[20]  Christel Baier,et al.  Model checking performability properties , 2002, Proceedings International Conference on Dependable Systems and Networks.

[22]  Joost-Pieter Katoen,et al.  Approximate Model Checking of Stochastic Hybrid Systems , 2010, Eur. J. Control.

[23]  Joost-Pieter Katoen,et al.  Model checking Markov reward models with impulse rewards , 2005, 2005 International Conference on Dependable Systems and Networks (DSN'05).

[24]  Holger Hermanns,et al.  A Markov Chain Model Checker , 2000, TACAS.

[25]  Susanna Donatelli,et al.  Verifying Stochastic Well-formed Nets with CSL Model-Checking Tools , 2006, Sixth International Conference on Application of Concurrency to System Design (ACSD'06).

[26]  Christel Baier,et al.  Model-Checking Algorithms for Continuous-Time Markov Chains , 2002, IEEE Trans. Software Eng..

[27]  Sergio Pissanetzky,et al.  Sparse Matrix Technology , 1984 .

[28]  Robert E. Tarjan,et al.  Self-adjusting binary search trees , 1985, JACM.

[29]  Stephen Gilmore,et al.  A New Generation PEPA Workbench , 2006 .

[30]  D. Iglehart,et al.  Discrete time methods for simulating continuous time Markov chains , 1976, Advances in Applied Probability.

[31]  Lijun Zhang,et al.  Probabilistic CEGAR , 2008, CAV.

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

[33]  William H. Sanders,et al.  A new methodology for calculating distributions of reward accumulated during a finite interval , 1996, Proceedings of Annual Symposium on Fault Tolerant Computing.

[34]  Sven Johr,et al.  Model checking compositional Markov systems , 2008 .

[35]  Jon Louis Bentley,et al.  Engineering a sort function , 1993, Softw. Pract. Exp..

[36]  Susanna Donatelli,et al.  Compositionality in the GreatSPN tool and its application to the modelling of industrial applications , 2000 .

[37]  Christel Baier,et al.  On the Logical Characterisation of Performability Properties , 2000, ICALP.

[38]  Gerald S. Shedler.  Regenerative Stochastic Simulation , 1992 .

[39]  Holger Hermanns,et al.  Interactive Markov Chains , 2002, Lecture Notes in Computer Science.

[40]  Joost-Pieter Katoen,et al.  Bisimulation Minimisation Mostly Speeds Up Probabilistic Model Checking , 2007, TACAS.

[41]  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.

[42]  Enrico Tronci,et al.  Finite horizon analysis of Markov Chains with the Murϕ verifier , 2006, International Journal on Software Tools for Technology Transfer.

[43]  William H. Sanders,et al.  Solution of Large Markov Models Using Lumping Techniques and Symbolic Data Structures , 2005 .

[44]  A. Nádas.  An Extension of a Theorem of Chow and Robbins on Sequential Confidence Intervals for the Mean , 1969 .

[45]  Giuliana Franceschinis,et al.  Simple O(m logn) Time Markov Chain Lumping , 2010, TACAS.

[46]  Holger Hermanns,et al.  Uniformity by Construction in the Analysis of Nondeterministic Stochastic Systems , 2007, 37th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN'07).

[47]  Gianfranco Ciardo,et al.  Logical and Stochastic Modeling with SMART , 2003, Computer Performance Evaluation / TOOLS.

[48]  M.A. Qureshi,et al.  The UltraSAN Modeling Environment , 1995, Perform. Evaluation.

[49]  Bernd Becker,et al.  Compositional Performability Evaluation for STATEMATE , 2006, Third International Conference on the Quantitative Evaluation of Systems - (QEST'06).

[50]  Christel Baier,et al.  Efficient Computation of Time-Bounded Reachability Probabilities in Uniform Continuous-Time Markov Decision Processes , 2005, TACAS.

[51]  Henk C. Tijms,et al.  A fast algorithm for the transient reward distribution in continuous-time Markov chains , 2000, Oper. Res. Lett..

[52]  Kishor S. Trivedi,et al.  STIFFNESS-TOLERANT METHODS FOR TRANSIENT ANALYSIS OF STIFF MARKOV CHAINS , 1994 .

[53]  Marta Z. Kwiatkowska,et al.  Symmetry Reduction for Probabilistic Model Checking , 2006, CAV.

[54]  Joost-Pieter Katoen,et al.  Safe On-The-Fly Steady-State Detection for Time-Bounded Reachability , 2005, Third International Conference on the Quantitative Evaluation of Systems - (QEST'06).

[55]  Håkan L. S. Younes,et al.  Statistical probabilistic model checking with a focus on time-bounded properties , 2006, Inf. Comput..

[56]  Thomas Hérault,et al.  APMC 3.0: Approximate Verification of Discrete and Continuous Time Markov Chains , 2006, Third International Conference on the Quantitative Evaluation of Systems - (QEST'06).

[57]  William H. Sanders,et al.  Optimal state-space lumping in Markov chains , 2003, Inf. Process. Lett..

[58]  Franck van Breugel,et al.  Probabilistic Model Checking with Java PathFinder , 2010 .

[59]  Alexander Bell.  Distributed Evaluation of Stochastic Petri nets , 2004, MMB.