True-concurrency probabilistic models: Markov nets and a law of large numbers

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 a branching...

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Bibliographic Details
Published inTheoretical computer science Vol. 390; no. 2; pp. 129 - 170
Main Authors Abbes, Samy, Benveniste, Albert
Format Journal Article Conference Proceeding
LanguageEnglish
Published Amsterdam Elsevier B.V 28.01.2008
Elsevier
Subjects
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Language theory and syntactical analysis
Miscellaneous
Probabilistic event structure
Probabilistic Petri net
Probability
Theoretical computing
True-concurrency
Probability
Probabilistic event structure
True-concurrency
Probabilistic Petri net
Branching
Cell structure
Computer theory
Asymptotic behavior
Probability distribution
Markov model
Characterization
Trace
Concurrency
Semantics
Probabilistic model
Event structure
Petri net
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Summary: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 a branching cell for event structures, and show that the latter provides an adequate conception 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 for the characterization, in a quantitative way, of the asymptotic behavior of Markov nets.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2007.09.018