Branching processes of Petri nets
Acta Informatica
Probability
Randomized Non-sequential Processes
CONCUR '01 Proceedings of the 12th International Conference on Concurrency Theory
Petri Nets for Systems Engineering: A Guide to Modeling, Verification, and Applications
Petri Nets for Systems Engineering: A Guide to Modeling, Verification, and Applications
Branching cells as local states for event structures and nets: probabilistic applications
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
Probabilistic Configuration Theories
Electronic Notes in Theoretical Computer Science (ENTCS)
True-concurrency probabilistic models: Markov nets and a law of large numbers
Theoretical Computer Science
Concurrency, σ -Algebras, and Probabilistic Fairness
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Taming confusion for modeling and implementing probabilistic concurrent systems
ESOP'13 Proceedings of the 22nd European conference on Programming Languages and Systems
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We study probabilistic safe Petri nets, a probabilistic extension of safe Petri nets interpreted under the true-concurrent semantics. In particular, the likelihood of processes is defined on partial orders, not on firing sequences. We focus on memoryless probabilistic nets: we give a definition for such systems, that we call Markov nets, and we study their properties. We show that several tools from Markov chains theory can be adapted to this true-concurrent framework. In particular, we introduce stopping operators that generalize stopping times, in a more convenient fashion than other extensions previously proposed. A Strong Markov Property holds in the concurrency framework. We show that the Concurrent Strong Markov property is the key ingredient for studying the dynamics of Markov nets. In particular we introduce some elements of a recurrence theory for nets, through the study of renewal operators. Due to the concurrency properties of Petri nets, Markov nets have global and local renewal operators, whereas both coincide for sequential systems.