Date of Submission

Spring 2023

Academic Program

Computer Science; Mathematics

Project Advisor 1

Bob McGrail

Project Advisor 2

Caitlin Leverson

Abstract/Artist's Statement

The purpose of this project is to show that quandle unification reduces to quandle matching. We show that any unification problem $U$ can be embedded into a matching problem $M$. If a unifier exists for $M$, then the narrowing sequence $N$ of that unifier can be refactored to $N'$ such that all of its idempotence narrowing steps involving substitutions are done last. At the moment when the narrowing sequence $N'$ needs only to do idempotence steps to unify $M$, we show that this implies a form for the embedded matching problem $U$ such that $U$ is guaranteed to have a unifier. This result also verifies that a quandle unification algorithm which uses the embedding technique is solving unification and not just matching.

Open Access Agreement

Open Access

Creative Commons License

Creative Commons License
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