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Unordered Constraint Satisfaction Games

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7464)

Abstract

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).

Keywords

  • 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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Ahlroth, L., Orponen, P. (2012). Unordered Constraint Satisfaction Games. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_9

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  • DOI: https://doi.org/10.1007/978-3-642-32589-2_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32588-5

  • Online ISBN: 978-3-642-32589-2

  • eBook Packages: Computer ScienceComputer Science (R0)