Rewriting systems, plain groups, and geodetic graphs

Murray Elder; Adam Piggott

doi:10.1016/j.tcs.2021.12.022

Rewriting systems, plain groups, and geodetic graphs

Murray Elder^*, Adam Piggott

^*Corresponding author for this work

Mathematical Sciences Institute

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We take a new step towards an algebraic characterisation of groups presented by length-reducing rewriting systems. We prove that a group is presented by finite convergent length-reducing rewriting systems where each rule has left-hand side of length three if and only if the group is plain.

Our proof rests on proving a new result about embedded circuits in geodetic graphs, whose proof may also be of independent interest to graph theorists.

Original language	English
Pages (from-to)	134-144
Number of pages	11
Journal	Theoretical Computer Science
Volume	903
DOIs	https://doi.org/10.1016/j.tcs.2021.12.022
Publication status	Published - 8 Feb 2022

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abstract = "We take a new step towards an algebraic characterisation of groups presented by length-reducing rewriting systems. We prove that a group is presented by finite convergent length-reducing rewriting systems where each rule has left-hand side of length three if and only if the group is plain.Our proof rests on proving a new result about embedded circuits in geodetic graphs, whose proof may also be of independent interest to graph theorists.",

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N2 - We take a new step towards an algebraic characterisation of groups presented by length-reducing rewriting systems. We prove that a group is presented by finite convergent length-reducing rewriting systems where each rule has left-hand side of length three if and only if the group is plain.Our proof rests on proving a new result about embedded circuits in geodetic graphs, whose proof may also be of independent interest to graph theorists.

AB - We take a new step towards an algebraic characterisation of groups presented by length-reducing rewriting systems. We prove that a group is presented by finite convergent length-reducing rewriting systems where each rule has left-hand side of length three if and only if the group is plain.Our proof rests on proving a new result about embedded circuits in geodetic graphs, whose proof may also be of independent interest to graph theorists.

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JO - Theoretical Computer Science

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Rewriting systems, plain groups, and geodetic graphs

Abstract

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