Reduction Operators and Completion of Rewriting Systems - Archive ouverte HAL
Preprints, Working Papers, ... Year : 2016

Reduction Operators and Completion of Rewriting Systems

Abstract

We propose a functional description of rewriting systems where reduction rules are represented by linear maps called reduction operators. We show that reduction operators admit a lattice structure. Using this structure we define the notions of confluence and of Church-Rosser property. We show that these notions are equivalent. We give an algebraic formulation of completion and show that such a completion exists using the lattice structure. We interpret the confluence for reduction operators in terms of Gröbner bases. Finally, we introduce generalised reduction operators relative to non totally ordered sets.
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Dates and versions

hal-01325907 , version 1 (02-06-2016)
hal-01325907 , version 2 (20-02-2017)

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Cyrille Chenavier. Reduction Operators and Completion of Rewriting Systems. 2016. ⟨hal-01325907v1⟩
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