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Lumping-based equivalences in Markovian automata: algorithms and applications to product-form analyses. (English) Zbl 1390.68371
Summary: In this paper we consider two relations over stochastic automata, named lumpable bisimulation and exact equivalence, that induce a strong and an exact lumping, respectively, on the underlying Markov chains. We show that an exact equivalence over the states of a non-synchronising automaton is indeed a lumpable bisimulation for the corresponding reversed automaton and then it induces a strong lumping on the time-reversed Markov chain underlying the model. This property allows us to prove that the class of quasi-reversible models is closed under exact equivalence. Quasi-reversibility is a pivotal property to study product-form models. Hence, exact equivalence turns out to be a theoretical tool to prove the product-form of models by showing that they are exactly equivalent to models which are known to be quasi-reversible. Algorithms for computing both lumpable bisimulation and exact equivalence are introduced. Case studies as well as performance tests are also presented.

MSC:
68Q45 Formal languages and automata
68Q87 Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)
Software:
SPADES; ipc
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