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Unordered Constraint Satisfaction Games

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Book cover Mathematical Foundations of Computer Science 2012 (MFCS 2012)

Part of the book series: Lecture Notes in Computer Science ((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).

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Author information

Authors and Affiliations

  1. Department of Information and Computer Science and, Helsinki Institute for Information Technology HIIT, Aalto University, Finland

    Lauri Ahlroth & Pekka Orponen

Authors
  1. Lauri Ahlroth
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  2. Pekka Orponen
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynska Dolina, 84248, Bratislava, Slovakia

    Branislav Rovan

  2. Department of Electronics and Computer Science, University of Southampton, SO17 1BJ, Southampton, UK

    Vladimiro Sassone

  3. Institute of Theoretical Computer Science, ETH Zürich, CAB H 39.2, Universitätstrasse 6, 8092, Zürich, Switzerland

    Peter Widmayer

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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

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