Date of Submission
Computer Science; Mathematics
Project Advisor 1
Project Advisor 2
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.
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Redman, Maximus, "Quandle Unification Reduces to Quandle Matching" (2023). Senior Projects Spring 2023. 257.
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