Algebraic Structure of Combined Traces

TL;DR

This paper explores the algebraic structure of combined traces, extending formal models for analyzing concurrent systems, introducing new notions, algorithms, and representations to improve understanding and processing of comtraces.

Contribution

It develops fundamental notions for combined traces, including indivisible steps and canonical forms, and provides algorithms for step sequence equivalence, advancing the theoretical framework of comtraces.

Findings

Introduced the lexicographical canonical form of comtraces

Developed algorithms for step sequence equivalence in comtraces

Established foundational notions for future development of infinite comtraces

Abstract

Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are able to capture the notions of causality and simultaneity of atomic actions which take place during the process of a system's operation. The aim of this paper is a transfer to the domain of comtraces and developing of some fundamental notions, which proved to be successful in the theory of traces. In particular, we introduce and then apply the notion of indivisible steps, the lexicographical canonical form of comtraces, as well as the representation of a comtrace utilising its linear projections to binary action subalphabets. We also provide two algorithms related to the new notions. Using them, one can solve, in an efficient way, the problem of step sequence equivalence in the context of comtraces. One may view our results as a first step towards the development of infinite combined traces, as well as recognisable languages of combined traces.