Quantified constraint solving problems and finite two-player games: The QuaCode project

Page:

337-365

DOI:

https://doi.org/10.3166/RIA.31.337-365

OPEN ACCESS

Abstract:

Quantified Constraint Satisfaction Problems (QCSP) are a generalization of Constraint Satisfaction Problems (CSP) in which variables may be quantified existentially and universally. QCSP offers a natural framework to express PSPACE problems as finite two-player games with perfect information or planing under uncertainty. We present how QCSP may be used to model two-player games on three classical games : Nim game, MatrixGame and Connect Four. State-of-the-art QCSP solvers have an important drawback: they explore much larger combinatorial space than the natural search space of the original problem since they are unable to recognize that some sub-problems are necessarily true. We propose a very simple and elegant solution to use efficiently QCSP to design finite two-player games. Our QCSP solver built over GeCode, a CSP library, obtained very good results compared to state-of-the-art QCSP solvers.

Keywords:

*finite two-players game, quantified constraint satisfaction problem, QCSP*

1. Introduction

2. Problème de satisfaction de contraintes quantifiées

3. Exemples de jeux à deux joueurs à horizon fini modélisés en QCSP

4. Un solveur QCSP comme extension d’un solveur CSP

5. Solveur QCSP et jeux à deux joueurs à horizon fini

6. Le solveur QuaCode et l’état de l’art

7. Discussion

8. Perspectives et conclusion

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