Equivalence Relations for Stochastic Automata Networks

Stochastic Automata Networks (SANs) are an eecient 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 aaecting the results of an analysis. We consider equivalence according to several performance quantities and for stationary and transient analysis of SANs.