Deciding probabilistic automata weak bisimulation: theory and practice

Weak probabilistic bisimulation on probabilistic automata can be decided by an algorithm that needs to check a polynomial number of linear programming problems encoding weak transitions. It is hence of polynomial complexity. This paper discusses the specific complexity class of the weak probabilisti...

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Bibliographic Details
Published inFormal aspects of computing Vol. 28; no. 1; pp. 109 - 143
Main Authors Ferrer Fioriti, Luis María, Hashemi, Vahid, Hermanns, Holger, Turrini, Andrea
Format Journal Article
LanguageEnglish
Published London Springer London 01.03.2016
Association for Computing Machinery
Subjects
Algorithms
Complexity
Computer Science
Linear programming
Math Applications in Computer Science
Minimization
Optimization
Original Article
Polynomials
Probabilistic methods
Probability theory
Theory of Computation
Compositional analysis
Concurrency
Efficiency
Probabilistic automata
Weak bisimulation
Linear programming
Satisfiability modulo theories
Complexity
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Summary:Weak probabilistic bisimulation on probabilistic automata can be decided by an algorithm that needs to check a polynomial number of linear programming problems encoding weak transitions. It is hence of polynomial complexity. This paper discusses the specific complexity class of the weak probabilistic bisimulation problem, and it considers several practical algorithms and linear programming problem transformations that enable an efficient solution. We then discuss two different implementations of a probabilistic automata weak probabilistic bisimulation minimizer, one of them employing SAT modulo linear arithmetic as the solver technology. Empirical results demonstrate the effectiveness of the minimization approach on standard benchmarks, also highlighting the benefits of compositional minimization.
Bibliography:ObjectType-Article-1
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ISSN:0934-5043
1433-299X
DOI:10.1007/s00165-016-0356-4