Date of Submission

Spring 2020

Academic Program

Computer Science; Mathematics

Project Advisor 1

Robert McGrail

Project Advisor 2

Steven Simon

Abstract/Artist's Statement

This senior thesis attempts to determine the extent to which the P/NP dichotomy of finite algebras (as proven by Bulatov, et.al in 2017) can be cast in terms of connectedness in Cayley graphs. This research is motivated by Prof. Robert McGrail's work ``CSPs and Connectedness: P/NP-Complete Dichotomy for Idempotent, Right Quasigroups" published in 2014 in which he demonstrates the strong correspondence between tractability and total path-connectivity in Cayley graphs for right, idempotent quasigroups. In particular, we will introduce the notion of total V-connectedness and show how it could be potentially used to phrase the dichotomy in terms of connectivity for another class of algebras, namely for Quay algebras.

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