Concurrency and Probability: Removing Confusion, Compositionally.

HERNÁN MELGRATTI; UGO MONTANARI; ROBERTO BRUNI

Oxford

Conferencia; Thirty-Third Annual ACM/IEEE Symposium on Logic in Computer Science (LICS); 2018

ACM/IEEE

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 con icting alternatives can be equipped with probabilistic choices, while nonintersecting al- ternatives are purely concurrent and their probability distributions are independent. The validity of the construction is witnessed by a tight correspondence with the recursively stopped con gurations of Abbes and Benveniste. Some advantages of our approach are that: i) s-cells are de ned statically and locally in a compositional way; ii) our resulting nets faithfully account for concurrency