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Extending linear rewriting modulo beyond monomial-invertible rules

Develop a theory of linear rewriting modulo that permits non-monomial modulo rules (such as relations of the form b ∼ b1 + b2), extending the current framework—which requires monomial-invertible modulo—while preserving practical criteria for termination, (tamed) confluence, and basis extraction.

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Background

The thesis develops linear Gray rewriting modulo under the restriction that modulo relations are monomial-invertible (i.e., rewrite monomials to scalar multiples of monomials).

Allowing more general modulo rules would significantly broaden applicability, but would require new techniques to control termination and confluence in the presence of scalar and linear combinations.

References

We stress that in our approach, the modulo data in linear rewriting modulo must be monomial-invertible. In other words, while it incorporates multiplication by an invertible scalar, a relation such as b ∼ b +b for distinct monomials b, b is not a valid modulo rule. Extending our work to this more general setting is an important open problem.

— Odd Khovanov homology, higher representation theory and higher rewriting theory (2410.11405 - Schelstraete, 15 Oct 2024) in Section ii.2.3 Special cases — Limitation