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.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Recommended Citation
Redman, Maximus, "Quandle Unification Reduces to Quandle Matching" (2023). Senior Projects Spring 2023. 257.
https://digitalcommons.bard.edu/senproj_s2023/257
This work is protected by a Creative Commons license. Any use not permitted under that license is prohibited.
