Bruni, Roberto and Melgratti, Hernán and Montanari, Ugo - Concurrency and Probability: Removing Confusion, Compositionally

lmcs:5271 - Logical Methods in Computer Science, December 19, 2019, Volume 15, Issue 4
Concurrency and Probability: Removing Confusion, Compositionally

Authors: Bruni, Roberto and Melgratti, Hernán and Montanari, Ugo

Assigning a satisfactory truly concurrent semantics to Petri nets with confusion and distributed decisions is a long standing problem, especially if one wants to resolve decisions by drawing from some probability distribution. Here we propose a general solution based on a recursive, static decomposition of (occurrence) nets in loci of decision, called structural branching cells (s-cells). Each s-cell exposes a set of alternatives, called transactions. Our solution transforms a given Petri net into another net whose transitions are the transactions of the s-cells and whose places are those of the original net, with some auxiliary structure for bookkeeping. The resulting net is confusion-free, and thus conflicting alternatives can be equipped with probabilistic choices, while nonintersecting alternatives are purely concurrent and their probability distributions are independent. The validity of the construction is witnessed by a tight correspondence with the recursively stopped configurations of Abbes and Benveniste. Some advantages of our approach are that: i) s-cells are defined statically and locally in a compositional way; ii) our resulting nets faithfully account for concurrency.


Source : oai:arXiv.org:1710.04570
Volume: Volume 15, Issue 4
Published on: December 19, 2019
Submitted on: March 8, 2019
Keywords: Computer Science - Logic in Computer Science,F.1.1, F.1.2,F.1.1,F.1.2


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