A Characterization of Combined Traces Using Labeled Stratified Order Structures

TL;DR

This paper introduces a new labeled stratified order structure that precisely characterizes combined traces (comtraces), providing equivalent representations through quotient monoids, dependency graphs, and stratified order structures.

Contribution

It offers a novel characterization of comtraces using labeled stratified order structures and proves their equivalence with existing representations.

Findings

Established representation theorems for comtraces

Proved equivalence of three different comtrace representations

Enhanced understanding of the algebraic and graph-based models

Abstract

This paper defines a class of labeled stratified order structures that characterizes exactly the notion of combined traces (i.e., comtraces) proposed by Janicki and Koutny in 1995. Our main technical contributions are the representation theorems showing that comtrace quotient monoid, combined dependency graph (Kleijn and Koutny 2008) and our labeled stratified order structure characterization are three different and yet equivalent ways to represent comtraces.