The trace monoids in the queue monoid and in the direct product of two free monoids

TL;DR

This paper establishes a precise relationship between trace monoids and queue monoids, showing that embedding into one corresponds to embedding into a specific product of free monoids, with a decidable characterization provided.

Contribution

It proves that a trace monoid embeds into the queue monoid if and only if it embeds into the direct product of two free monoids, offering a new decidable criterion.

Findings

Embedding into the queue monoid is equivalent to embedding into the direct product of two free monoids.

Provides a decidable characterization of trace monoids that embed into these structures.

Establishes a fundamental connection between trace monoids, queue monoids, and free monoids.

Abstract

We prove that a trace monoid embeds into the queue monoid if and only if it embeds into the direct product of two free monoids. We also give a decidable characterization of these trace monoids.