Simulation for Interactive Markov Chains

Interactive Markov chains (IMCs) are compositional performance evaluation models which can be used to powerfully model concurrent systems. Simulations that are abstracted from internal computation have been proven to be useful for verification of compositely defined transition system. In the literature of stochastic extension of this transition system, computing simulation preorders are rare. In this paper strong(weak) simulation is introduced for IMCs. The main result of the paper is that we give algorithms to decide strong(weak) simulation preorder for IMCs with a polynomial-time complexity in the number of states of the transition system.

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

[2]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[3]  R. Milner,et al.  Bigraphical Reactive Systems , 2001, CONCUR.

[4]  Carla Piazza,et al.  Simulation as Coarsest Partition Problem , 2002, TACAS.

[5]  Thomas A. Henzinger,et al.  Computing simulations on finite and infinite graphs , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[6]  Rainer Hegselmann,et al.  Opinion dynamics and bounded confidence: models, analysis and simulation , 2002, J. Artif. Soc. Soc. Simul..

[7]  Bengt Jonsson.  Simulations Between Specifications of Distributed Systems , 1991, CONCUR.

[8]  Robert E. Tarjan,et al.  Three Partition Refinement Algorithms , 1987, SIAM J. Comput..

[9]  Scott A. Smolka,et al.  CCS expressions, finite state processes, and three problems of equivalence , 1983, PODC '83.

[10]  Rance Cleaveland,et al.  Simulation Revisited , 2001, TACAS.

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

[12]  Jinzhao Wu,et al.  Analysis & Tools: Stochastic Analysis , 2005 .

[13]  Joost-Pieter Katoen,et al.  Towards Model Checking Stochastic Process Algebra , 2000, IFM.

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

[15]  Christel Baier,et al.  Comparative Branching-Time Semantics , 2003, CONCUR.

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

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

[18]  Christel Baier,et al.  Simulation for Continuous-Time Markov Chains , 2002, CONCUR.

[19]  Insup Lee,et al.  Weak Bisimulation for Probabilistic Systems , 2000, CONCUR.

[20]  Christel Baier,et al.  Weak Bisimulation for Fully Probabilistic Processes , 1997, FBT.

[21]  Kousha Etessami,et al.  Optimizing Büchi Automata , 2000, CONCUR.

[22]  Scott A. Smolka,et al.  Fundamental Results for the Verification of Observational Equivalence: A Survey , 1987, PSTV.

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

[24]  Cnrs Fre,et al.  Model Checking a Path (Preliminary Report) , 2003 .

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

[26]  Kousha Etessami,et al.  A Hierarchy of Polynomial-Time Computable Simulations for Automata , 2002, CONCUR.

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

[28]  Rance Cleaveland,et al.  A Semantics Based Verification Tool for Finite State Systems , 1989, PSTV.

[29]  Joost-Pieter Katoen,et al.  Performance Evaluation : = (Process Algebra + Model Checking) × Markov Chains , 2001, CONCUR.