On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids

Cain, Alan J., Gray, Robert D. and Malheiro, António (2017) On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids. Information and Computation, 255 (1). pp. 68-93. ISSN 0890-5401

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    Abstract

    This paper investigates the class of finitely presented monoids defined by homogeneous (length-preserving) relations from a computational perspective. The properties of admitting a finite complete rewriting system, having finite derivation type, being automatic, and being biautomatic are investigated for this class of monoids. The first main result shows that for any consistent combination of these properties and their negations, there is a homogeneous monoid with exactly this combination of properties. We then introduce the new concept of abstract Rees-commensurability (an analogue of the notion of abstract commensurability for groups) in order to extend this result to show that the same statement holds even if one restricts attention to the class of n-ary homogeneous monoids (where every side of every relation has fixed length n). We then introduce a new encoding technique that allows us to extend the result partially to the class of n-ary multihomogenous monoids.

    Item Type: Article
    Uncontrolled Keywords: homogeneous monoid,presentation,rewriting system,homotopy,finite derivation type,automatic,biautomatic
    Faculty \ School: Faculty of Science > School of Mathematics
    Depositing User: Pure Connector
    Date Deposited: 31 May 2017 09:31
    Last Modified: 09 Apr 2019 12:15
    URI: https://ueaeprints.uea.ac.uk/id/eprint/63619
    DOI: 10.1016/j.ic.2017.05.003

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