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

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

Vincent Barichard Igor Stéphan 

Université d’Angers, 2 boulevard Lavoisier, 49045 Angers, France

Corresponding Author Email: 
vincent.barichard@univ-angers.fr; igor.stephan@univ-angers.fr
Page: 
337-365
|
DOI: 
https://doi.org/10.3166/RIA.31.337-365
Received: 
|
Accepted: 
|
Published: 
30 June 2017
| Citation

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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