Representation of traces by vectors of words

TL;DR

This paper demonstrates that trace monoids can be represented as sub-monoids of word vector monoids, offering a concrete process-based visualization and insights into their ordering structure.

Contribution

It introduces a novel representation of trace monoids as sub-monoids of word vector monoids, linking algebraic structures to process models.

Findings

Trace monoids are isomorphic to sub-monoids of word vector monoids.

Provides a concrete process-based representation of trace elements.

Results on the ordering structure of the left divisibility relation.

Abstract

We show that every trace monoid is isomorphic to a sub-monoid of a monoid of word vectors. It provides a concrete representation of the elements of a trace monoid as processes associated with a resource sharing mechanism. We illustrate this representation by obtaining some results on the ordering structure of the left divisibility relation on trace monoids.