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.
Research partially supported by German Research Foundation (DFG) funded SFB 805.
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Ederer, T., Lorenz, U., Opfer, T., Wolf, J. (2012). Modeling Games with the Help of Quantified Integer Linear Programs. In: van den Herik, H.J., Plaat, A. (eds) Advances in Computer Games. ACG 2011. Lecture Notes in Computer Science, vol 7168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31866-5_23
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