When Equivalence and Bisimulation Join Forces in Probabilistic Automata

Probabilistic automata were introduced by Rabin in 1963 as language acceptors. Two automata are equivalent if and only if they accept each word with the same probability. On the other side, in the process algebra community, probabilistic automata were re-proposed by Segala in 1995 which are more general than Rabin's automata. Bisimulations have been proposed for Segala's automata to characterize the equivalence between them. So far the two notions of equivalences and their characteristics have been studied most independently. In this paper, we consider Segala's automata, and propose a novel notion of distribution-based bisimulation by joining the existing equivalence and bisimilarities. Our bisimulation bridges the two closely related concepts in the community, and provides a uniform way of studying their characteristics. We demonstrate the utility of our definition by studying distribution-based bisimulation metrics, which gives rise to a robust notion of equivalence for Rabin's automata.

[1]  Yi Li,et al.  A Web-Based Probabilistic Model Checker ? , 2014 .

[2]  Mingsheng Ying.  Bisimulation indexes and their applications , 2002, Theor. Comput. Sci..

[3]  Doina Precup,et al.  On-the-Fly Algorithms for Bisimulation Metrics , 2012, 2012 Ninth International Conference on Quantitative Evaluation of Systems.

[4]  Yi Li,et al.  iscasMc: A Web-Based Probabilistic Model Checker , 2014, FM.

[5]  Rupak Majumdar,et al.  Game Relations and Metrics , 2007, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007).

[6]  Alan F. Blackwell,et al.  Programming , 1973, CSC '73.

[7]  Kim G. Larsen,et al.  On-the-Fly Exact Computation of Bisimilarity Distances , 2013, TACAS.

[8]  Carroll Morgan,et al.  Testing Finitary Probabilistic Processes , 2009, CONCUR.

[9]  Roberto Segala,et al.  Decision Algorithms for Probabilistic Bisimulation , 2002, CONCUR.

[10]  Lijun Zhang,et al.  On Probabilistic Automata in Continuous Time , 2010, 2010 25th Annual IEEE Symposium on Logic in Computer Science.

[11]  Christel Baier,et al.  Probabilistic ω-automata , 2012, JACM.

[12]  Joël Ouaknine,et al.  On the Complexity of the Equivalence Problem for Probabilistic Automata , 2011, FoSSaCS.

[13]  James Worrell,et al.  Approximating a Behavioural Pseudometric without Discount for Probabilistic Systems , 2007, Log. Methods Comput. Sci..

[14]  Krishnendu Chatterjee,et al.  Algorithms for Game Metrics , 2008, FSTTCS.

[15]  Hongfei Fu,et al.  Computing Game Metrics on Markov Decision Processes , 2012, ICALP.

[16]  Marta Z. Kwiatkowska,et al.  PRISM 4.0: Verification of Probabilistic Real-Time Systems , 2011, CAV.

[17]  Joël Ouaknine,et al.  Language Equivalence for Probabilistic Automata , 2011, CAV.

[18]  Mingsheng Ying.  Topology in process calculus - approximate correctness and infinite evolution of concurrent programs , 2001 .

[19]  Krishnendu Chatterjee,et al.  Algorithms for Game Metrics (Full Version) , 2008, Log. Methods Comput. Sci..

[20]  Thomas A. Henzinger,et al.  Equivalence of Labeled Markov Chains , 2008, Int. J. Found. Comput. Sci..

[21]  Radha Jagadeesan,et al.  Metrics for labelled Markov processes , 2004, Theor. Comput. Sci..

[22]  Wen-Guey Tzeng,et al.  A Polynomial-Time Algorithm for the Equivalence of Probabilistic Automata , 1992, SIAM J. Comput..

[23]  R. Bellman.  Dynamic programming. , 1957, Science.

[24]  Radha Jagadeesan,et al.  Metrics for Labeled Markov Systems , 1999, CONCUR.

[25]  Radha Jagadeesan,et al.  Weak bisimulation is sound and complete for pCTL* , 2002, Inf. Comput..

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

[27]  James Worrell,et al.  On the Complexity of Computing Probabilistic Bisimilarity , 2012, FoSSaCS.

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

[29]  Doina Precup,et al.  Bisimulation Metrics for Continuous Markov Decision Processes , 2011, SIAM J. Comput..

[30]  Roberto Segala,et al.  Logical Characterizations of Bisimulations for Discrete Probabilistic Systems , 2007, FoSSaCS.

[31]  Lijun Zhang,et al.  Probabilistic Logical Characterization , 2011, Inf. Comput..

[32]  François Laviolette,et al.  Approximate Analysis of Probabilistic Processes: Logic, Simulation and Games , 2008, 2008 Fifth International Conference on Quantitative Evaluation of Systems.

[33]  Martin Wirsing,et al.  Approximate Bisimilarity , 2000, AMAST.

[34]  Scott A. Smolka,et al.  Algebraic Reasoning for Probabilistic Concurrent Systems , 1990, Programming Concepts and Methods.

[35]  Holger Hermanns,et al.  Deciding Probabilistic Automata Weak Bisimulation in Polynomial Time , 2012, FSTTCS.

[36]  Azaria Paz,et al.  Probabilistic automata , 2003 .

[37]  Matthew Hennessy.  Exploring probabilistic bisimulations, part I , 2012, Formal Aspects of Computing.

[38]  Joost-Pieter Katoen,et al.  The Ins and Outs of the Probabilistic Model Checker MRMC , 2009, 2009 Sixth International Conference on the Quantitative Evaluation of Systems.