Equivalence Relations for Stochastic Automata Networks

Peter Buchholz
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Peter Buchholz: Universität Dortmund, Informatik IV

Chapter 13 in Computations with Markov Chains, 1995, pp 197-215 from Springer

Abstract: Abstract Stochastic Automata Networks (SANs) are an efficient means to describe and analyze parallel systems under Markovian assumptions. The main advantage of SANs is the possibility to describe and analyze a complex parallel system in a compositional way such that the transition matrix of the Markov chain underlying the complete SAN can be described in a compositional way using only small matrices specifying single automata and combine these matrices by means of tensor operations. This approach allows, up to a certain extent, the handling of the state space explosion resulting from complex Markov models. In this paper equivalence relations for stochastic automata are introduced such that an automaton in a network can be substituted by an equivalent and usually smaller automaton without affecting the results of an analysis. We consider equivalence according to stationary and transient analysis of SANs.

Keywords: Equivalence Class; Equivalence Relation; Transition Rate; State Space Explosion; Finite Markov Chain (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-1-4615-2241-6_13

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