Toward uniform random generation in 1-safe Petri nets

Samy Abbes

doi:10.1016/j.endm.2017.05.002

Abstract

We study the notion of uniform measure on the space of infinite executions of a 1-safe Petri net. Here, executions of 1-safe Petri nets are understood up to commutation of concurrent transitions, which introduces a challenge compared to usual transition systems. We obtain that the random generation of infinite executions reduces to the simulation of a finite state Markov chain. Algorithmic issues are discussed.

Highlights

Petri nets are formal models designed to describe and analyze the behavior of concurrent systems
Retaining only the last marking, we introduce the obvious notation M0 −t−1−···−t→k Mk, with the convention M0 −→ε M0 for the empty sequence ε, which is considered as a firing sequence
One way to obtain a sampling method is to consider the Markov chain of states-and-cliques, that is to say, the random sequence of pairs (Mk−1, Ck)k≥1, where (Ck)k≥1 is the sequence of cliques forming an infinite trace ξ and Mk is the marking reached after the kth clique

Summary

Introduction

Petri nets are formal models designed to describe and analyze the behavior of concurrent systems. We define R as the smallest congruence on the set firing sequences that contains all pairs (t · t , t · t), for t and t two distant transitions.

Objectives

Results

Conclusion