# Toward uniform random generation in 1-safe Petri nets

## TL;DR

This paper explores uniform random generation of infinite executions in 1-safe Petri nets, linking it to finite Markov chain simulation and addressing associated algorithmic challenges.

## Contribution

It introduces a method to generate infinite executions uniformly in 1-safe Petri nets by reducing the problem to finite Markov chain simulation.

## Key findings

- Uniform measure on infinite executions is characterized.
- Generation reduces to finite Markov chain simulation.
- Algorithmic approaches for simulation are discussed.

## 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.