Completion of operadic rewriting systems by Gaussian elimination
Résumé
We study the confluence properties of non-symmetric operadic rewriting systems using linear algebra methods. We extend the completion procedure F4, known for commutative and non-commutative algebras, to operads. This procedure allows us to parallelize completion by applying a Gaussian elimination process in order to treat multiple critical branchings simultaneously. We discuss heuristics and strategies to optimize this procedure in the operadic context: first to reduce the set of critical branchings to be examined and then to parallelize the elimination.
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