True-concurrency Probabilistic Models: Markov Nets and a Law
of Large Numbers
Samy Abbes and Albert Benveniste
We introduce the model of Markov nets, a probabilistic extension of
safe Petri nets under the true-concurrency semantics---this means that
traces, not firing sequences, are given a probability. This model
builds upon our previous work on probabilistic event structures. We use
the notion of branching cell for event structures and show that the
latter provides the adequate notion of local state, for nets. We
prove a Law of Large Numbers (LLN) for Markov nets, which constitutes
the main contribution of the paper. This LLN allows
characterizing in a quantitative way the asymptotic behavior of Markov
nets.
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