Correspondence between factorability and normalisation in monoids
Alen {\DJ}uri\'c
TL;DR
This paper explores the relationship between factorability structures and quadratic normalisation in monoids, providing axiomatic characterizations and conditions for termination of rewriting systems.
Contribution
It establishes a formal connection between factorability and quadratic normalisation, and characterizes quadratic normalisations of class (4,3) in terms of factorability.
Findings
Factorable monoids are characterized within quadratic normalisation axioms.
Quadratic normalisations of class (4,3) are characterized via factorability structures.
A condition for termination of the associated rewriting system is identified.
Abstract
Abstract. This article determines relations between two notions concerning monoids: factorability structure, introduced to simplify the bar complex; and quadratic normalisation, introduced to generalise quadratic rewriting systems and normalisations arising from Garside families. Factorable monoids are characterised in the axiomatic setting of quadratic normalisations. Additionally, quadratic normalisations of class (4,3) are characterised in terms of factorability structures and a condition ensuring the termination of the associated rewriting system.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Logic, programming, and type systems