A Combinatorial Problem Which Is Complete in Polynomial Space
Journal of the ACM (JACM)
Alternating-time temporal logic
Journal of the ACM (JACM)
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
Playing Games with Algorithms: Algorithmic Combinatorial Game Theory
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Complexity, appeal and challenges of combinatorial games
Theoretical Computer Science - Algorithmic combinatorial game theory
Quantified Constraint Optimization
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
The complexity of constraint satisfaction games and QCSP
Information and Computation
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
QCSP made practical by virtue of restricted quantification
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
A Tetrachotomy for Positive First-Order Logic without Equality
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
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We consider two-player constraint satisfaction games on systems of Boolean constraints, in which the players take turns in selecting one of the available variables and setting it to true or false, with the goal of maximising (for Player I) or minimising (for Player II) the number of satisfied constraints. Unlike in standard QBF-type variable assignment games, we impose no order in which the variables are to be played. This makes the game setup more natural, but also more challenging to control. We provide polynomial-time, constant-factor approximation strategies for Player I when the constraints are parity functions or threshold functions with a threshold that is small compared to the arity of the constraints. Also, we prove that the problem of determining if Player I can satisfy all constraints is PSPACE-complete even in this unordered setting, and when the constraints are disjunctions of at most 6 literals (an unordered-game analogue of 6-QBF).