Uniform generation in trace monoids

TL;DR

This paper investigates uniform random generation of traces in trace monoids, providing a product decomposition of the uniform measure at infinity for monoids with multiple irreducible components and analyzing related algorithms.

Contribution

It introduces a novel product decomposition of the uniform measure at infinity for complex trace monoids, enabling improved random generation methods.

Findings

Product decomposition of the uniform measure at infinity for trace monoids with multiple components

Development of random generation algorithms based on the measure decomposition

Extension of measure concepts where Parry measures are not defined

Abstract

We consider the problem of random uniform generation of traces (the elements of a free partially commutative monoid) in light of the uniform measure on the boundary at infinity of the associated monoid. We obtain a product decomposition of the uniform measure at infinity if the trace monoid has several irreducible components-a case where other notions such as Parry measures, are not defined. Random generation algorithms are then examined.