Concurrency and Probability: Removing Confusion, Compositionally

• Published in: Logical methods in computer science 2019-12, Vol.15, Issue 4
• Main Authors: Roberto Bruni, Hernán Melgratti, Ugo Montanari
• Format: Article
• Language: English
• Subjects: computer science - logic in computer science; f.1.1; f.1.1, f.1.2; f.1.2
• ISSN: 1860-5974
• DOI: 10.23638/LMCS-15(4:17)2019

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.