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Full-Text Articles in Discrete Mathematics and Combinatorics
Games For One, Games For Two: Computationally Complex Fun For Polynomial-Hierarchical Families, Kye Shi
Games For One, Games For Two: Computationally Complex Fun For Polynomial-Hierarchical Families, Kye Shi
HMC Senior Theses
In the first half of this thesis, we explore the polynomial-time hierarchy, emphasizing an intuitive perspective that associates decision problems in the polynomial hierarchy to combinatorial games with fixed numbers of turns. Specifically, problems in π are thought of as 0-turn games, ππ as 1-turn βpuzzleβ games, and in general πΊβπ as π-turn games, in which decision problems answer the binary question, βcan the starting player guarantee a win?β We introduce the formalisms of the polynomial hierarchy through this perspective, alongside definitions of π-turn CIRCUIT SATISFIABILITY games, whose πΊβπ-completeness is assumed from prior work (we briefly justify this assumption β¦