Modeling Games with the Help of Quantified Integer Linear Programs
Conference paper
Abstract
Quantified linear programs (QLPs) are linear programs with mathematical variables being either existentially or universally quantified. The integer variant (Quantified linear integer program, QIP) is PSPACE-complete, and can be interpreted as a two-person zero-sum game. Additionally, it demonstrates remarkable flexibility in polynomial reduction, such that many interesting practical problems can be elegantly modeled as QIPs. Indeed, the PSPACE-completeness guarantees that all PSPACE-complete problems such as games like Othello, Go-Moku, and Amazons, can be described with the help of QIPs, with only moderate overhead. In this paper, we present the Dynamic Graph Reliability (DGR) optimization problem and the game Go-Moku as examples.
Keywords
Integer Linear Program Mixed Integer Linear Programming Modeling Game Winning Strategy Universal Variable
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