Confluence of algebraic rewriting systems

Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical branching lemma that proves local confluence from confluence of th...

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Veröffentlicht in:Mathematical structures in computer science Jg. 32; H. 7; S. 870 - 897
Hauptverfasser: Chenavier, Cyrille, Dupont, Benjamin, Malbos, Philippe
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cambridge, UK Cambridge University Press 01.08.2022
Cambridge University Press (CUP)
Schlagworte:
Algebra
Axioms
Category Theory
Computer Science
Convergence
Data Structures and Algorithms
Group theory
Mathematics
Polygraphs
Special Issue: Confluence
Symbolic Computation
linear rewriting
Term rewriting modulo
algebraic polygraphs
group rewriting
string rewriting
ISSN:0960-1295, 1469-8072
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Zusammenfassung:Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical branching lemma that proves local confluence from confluence of the critical branchings. The analysis of local confluence of rewriting systems on algebraic structures, such as groups or linear algebras, is complicated because of the underlying algebraic axioms. This article introduces the structure of algebraic polygraph modulo that formalizes the interaction between the rules of an algebraic rewriting system and the inherent algebraic axioms, and we show a critical branching lemma for algebraic polygraphs. We deduce a critical branching lemma for rewriting systems on algebraic models whose axioms are specified by convergent modulo rewriting systems. We illustrate our constructions for string, linear, and group rewriting systems.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0960-1295
1469-8072
DOI:10.1017/S0960129521000426