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
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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