Unordered Constraint Satisfaction Games

  • Lauri Ahlroth
  • Pekka Orponen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)


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).


Constraint Satisfaction Constraint Satisfaction Problem Winning Strategy Boolean Formula Variable Swap 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Lauri Ahlroth
    • 1
  • Pekka Orponen
    • 1
  1. 1.Department of Information and Computer Science and, Helsinki Institute for Information Technology HIITAalto UniversityFinland

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