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 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 -- this 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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