Syzygies among reduction operators

Cyrille Chenavier 1, 2
2 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : We introduce the notion of syzygy for a set of reduction operators and relate it to the notion of syzygy for presentations of algebras. We give a method for constructing a linear basis of the space of syzygies for a set of reduction operators. We interpret these syzygies in terms of the confluence property from rewriting theory. This enables us to optimise the completion procedure for reduction operators based on a criterion for detecting useless reductions. We illustrate this criterion with an example of construction of commutative Gröbner basis.
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Submitted on : Monday, April 9, 2018 - 9:21:06 AM
Last modification on : Friday, April 19, 2019 - 4:54:58 PM


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  • HAL Id : hal-01578555, version 2
  • ARXIV : 1708.08709



Cyrille Chenavier. Syzygies among reduction operators. 2018. ⟨hal-01578555v2⟩



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