Unordered Constraint Satisfaction Games
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).
KeywordsConstraint Satisfaction Constraint Satisfaction Problem Winning Strategy Boolean Formula Variable Swap
Unable to display preview. Download preview PDF.
- 2.Ansótegui, C., Gomes, C.P., Selman, B.: The Achilles’ heel of QBF. In: Proc. 20th Natl. Conf. on Artificial Intelligence and 17th Conf. on Innovative Applications of Artificial Intelligence (AAAI/IAAI 2005), pp. 275–281 (2005)Google Scholar
- 3.Benedetti, M., Lallouet, A., Vautard, J.: QCSP made practical by virtue of restricted quantification. In: Proc. 20th Intl. Joint Conf. on Artificial Intelligence (IJCAI 2007), pp. 38–43 (2007)Google Scholar
- 9.Condon, A., Feigenbaum, J., Lund, C., Shor, P.W.: Probabilistically checkable debate systems and nonapproximability of PSPACE-hard functions. Chicago J. Theor. Comput. Sci. 4 (1995)Google Scholar
- 16.Madelaine, F.R., Martin, B.: A tetrachotomy for positive first-order logic without equality. In: Proc. 26th Ann. IEEE Symp. on Logic in Computer Science (LICS 2011), pp. 311–320 (2011)Google Scholar
- 19.Stockmeyer, L.J., Meyer, A.R.: Word problems requiring exponential time: Preliminary report. In: Proc. 5th Ann. ACM Symp. on Theory of Computing (STOC 1973), pp. 1–9 (1973)Google Scholar