A truly concurrent synchronization product of Markov chains
Résumé
In this paper we introduce a product operation on
labeled Markov chains. Whereas this kind of product is most usually
achieved under an interleaving semantics, for instance in the
framework of probabilistic automata, our construction stays within
the true-concurrent semantics. Hence the product of two
labeled Markov chains we define is a so-called
probabilistic Petri net, i.e. a safe Petri net where Mazurkiewicz
traces are randomized, not interleavings. We show that this
construction is not trivial as far as the number of synchronization
transitions is greater or equal than 2. Our main result is that the
product of Markov chains remains Markovian, in the sense of
probabilistic true-concurrent systems.
labeled Markov chains. Whereas this kind of product is most usually
achieved under an interleaving semantics, for instance in the
framework of probabilistic automata, our construction stays within
the true-concurrent semantics. Hence the product of two
labeled Markov chains we define is a so-called
probabilistic Petri net, i.e. a safe Petri net where Mazurkiewicz
traces are randomized, not interleavings. We show that this
construction is not trivial as far as the number of synchronization
transitions is greater or equal than 2. Our main result is that the
product of Markov chains remains Markovian, in the sense of
probabilistic true-concurrent systems.
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