Complete involute rewriting systems

Gareth A. Evans; Christopher D. Wensley

doi:10.1016/j.jsc.2007.07.005

Complete involute rewriting systems

Gareth A. Evans
, Christopher D. Wensley

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

Abstract

Given a monoid string rewriting system M, one way of obtaining a complete rewriting system for M is to use the classical Knuth–Bendix critical pairs completion algorithm. It is well-known that this algorithm is equivalent to computing a noncommutative Gröbner basis for M. This article develops an alternative approach, using noncommutative involutive basis methods to obtain a complete involutive rewriting system for M.

Original language	English
Pages (from-to)	1034-1051
Journal	Journal of Symbolic Computation
Volume	42
DOIs	https://doi.org/10.1016/j.jsc.2007.07.005
Publication status	Published - 2007

Keywords

Groebner basis, string rewriting, Knuth-Bendix, involute basis

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title = "Complete involute rewriting systems",

abstract = "Given a monoid string rewriting system M, one way of obtaining a complete rewriting system for M is to use the classical Knuth–Bendix critical pairs completion algorithm. It is well-known that this algorithm is equivalent to computing a noncommutative Gr{\"o}bner basis for M. This article develops an alternative approach, using noncommutative involutive basis methods to obtain a complete involutive rewriting system for M.",

keywords = "Groebner basis, string rewriting, Knuth-Bendix, involute basis",

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year = "2007",

doi = "10.1016/j.jsc.2007.07.005",

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T1 - Complete involute rewriting systems

AU - Evans, Gareth A.

AU - Wensley, Christopher D.

PY - 2007

Y1 - 2007

N2 - Given a monoid string rewriting system M, one way of obtaining a complete rewriting system for M is to use the classical Knuth–Bendix critical pairs completion algorithm. It is well-known that this algorithm is equivalent to computing a noncommutative Gröbner basis for M. This article develops an alternative approach, using noncommutative involutive basis methods to obtain a complete involutive rewriting system for M.

AB - Given a monoid string rewriting system M, one way of obtaining a complete rewriting system for M is to use the classical Knuth–Bendix critical pairs completion algorithm. It is well-known that this algorithm is equivalent to computing a noncommutative Gröbner basis for M. This article develops an alternative approach, using noncommutative involutive basis methods to obtain a complete involutive rewriting system for M.

KW - Groebner basis, string rewriting, Knuth-Bendix, involute basis

U2 - 10.1016/j.jsc.2007.07.005

DO - 10.1016/j.jsc.2007.07.005

M3 - Article

VL - 42

SP - 1034

EP - 1051

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

ER -

Complete involute rewriting systems

Abstract

Keywords

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