Probabilistic Logical Characterization

Probabilistic automata exhibit both probabilistic and non-deterministic choice. They are therefore a powerful semantic foundation for modeling concurrent systems with random phenomena arising in many applications ranging from artificial intelligence, security, systems biology to performance modeling. Several variations of bisimulation and simulation relations have proved to be useful as means to abstract and compare different automata. This paper develops a taxonomy of logical characterizations of these relations on image-finite and image-infinite probabilistic automata.

[1]  Christel Baier,et al.  Comparative branching-time semantics for Markov chains , 2005, Inf. Comput..

[2]  Augusto Parma.  Axiomatic and logical characterizations of probabilistic preorders and trace semantics , 2008 .

[3]  Prakash Panangaden,et al.  Labelled Markov Processes , 2009 .

[4]  Corina Cîrstea,et al.  Modular construction of complete coalgebraic logics , 2007, Theor. Comput. Sci..

[5]  Luca de Alfaro,et al.  Magnifying-Lens Abstraction for Markov Decision Processes , 2007, CAV.

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

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

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

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

[10]  Rob J. van Glabbeek,et al.  The Linear Time - Branching Time Spectrum II , 1993, CONCUR.

[11]  Radha Jagadeesan,et al.  Approximating labelled Markov processes , 2003, Inf. Comput..

[12]  Joost-Pieter Katoen,et al.  Bisimulation and Logical Preservation for Continuous-Time Markov Decision Processes , 2007, CONCUR.

[13]  Carroll Morgan,et al.  Characterising Testing Preorders for Finite Probabilistic Processes , 2007, LICS.

[14]  Radha Jagadeesan,et al.  Approximating labeled Markov processes , 2000, Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332).

[15]  Nancy A. Lynch,et al.  Analyzing Security Protocols Using Time-Bounded Task-PIOAs , 2008, Discret. Event Dyn. Syst..

[16]  Corina Cîrstea,et al.  Modal Logics are Coalgebraic , 2008, Comput. J..

[17]  Radha Jagadeesan,et al.  Weak Bisimulation is Sound and Complete for PCTL* , 2002, CONCUR.

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

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

[20]  Davide Sangiorgi.  Bisimulation: from the origins to today , 2004, LICS 2004.

[21]  Kim G. Larsen,et al.  Reduction and Refinement Strategies for Probabilistic Analysis , 2002, PAPM-PROBMIV.

[22]  Lutz Schröder,et al.  Expressivity of coalgebraic modal logic: The limits and beyond , 2008, Theor. Comput. Sci..

[23]  Roberto Segala,et al.  Comparative analysis of bisimulation relations on alternating and non-alternating probabilistic models , 2005, Second International Conference on the Quantitative Evaluation of Systems (QEST'05).

[24]  Prakash Panangaden,et al.  Continuous stochastic logic characterizes bisimulation of continuous-time Markov processes , 2003, J. Log. Algebraic Methods Program..

[25]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[26]  Corina Cîrstea,et al.  On Logics for Coalgebraic Simulation , 2004, CMCS.

[27]  Robin Milner,et al.  Algebraic laws for nondeterminism and concurrency , 1985, JACM.

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

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

[30]  Krishnendu Chatterjee,et al.  Model-Checking omega-Regular Properties of Interval Markov Chains , 2008, FoSSaCS.

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

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

[33]  Robert Givan,et al.  Equivalence notions and model minimization in Markov decision processes , 2003, Artif. Intell..

[34]  Rob J. van Glabbeek,et al.  The Linear Time - Branching Time Spectrum I , 2001, Handbook of Process Algebra.

[35]  Wang Yi,et al.  Probabilistic Extensions of Process Algebras , 2001, Handbook of Process Algebra.

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

[37]  Corina Cîrstea,et al.  A modular approach to defining and characterising notions of simulation , 2006, Inf. Comput..

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

[39]  Lijun Zhang,et al.  Decision algorithms for probabilistic simulations , 2009 .

[40]  Andrea Bianco,et al.  Model Checking of Probabalistic and Nondeterministic Systems , 1995, FSTTCS.

[41]  Bengt Jonsson,et al.  A calculus for communicating systems with time and probabilities , 1990, [1990] Proceedings 11th Real-Time Systems Symposium.

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

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

[44]  Kim Guldstrand Larsen,et al.  Specification and refinement of probabilistic processes , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.

[45]  Corina Cîrstea,et al.  A compositional approach to defining logics for coalgebras , 2004, Theor. Comput. Sci..

[46]  Abbas Edalat,et al.  Bisimulation for Labelled Markov Processes , 2002, Inf. Comput..

[47]  Nicolás Wolovick,et al.  Nondeterministic Labeled Markov Processes: Bisimulations and Logical Characterization , 2009, 2009 Sixth International Conference on the Quantitative Evaluation of Systems.

[48]  A. Tarski.  A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

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