6-Uniform Maker-Breaker Game Is PSPACE-Complete

Authors Md Lutfar Rahman, Thomas Watson

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Md Lutfar Rahman
  • University of Memphis, TN, USA
Thomas Watson
  • University of Memphis, TN, USA

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Md Lutfar Rahman and Thomas Watson. 6-Uniform Maker-Breaker Game Is PSPACE-Complete. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 57:1-57:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


In a STOC 1976 paper, Schaefer proved that it is PSPACE-complete to determine the winner of the so-called Maker-Breaker game on a given set system, even when every set has size at most 11. Since then, there has been no improvement on this result. We prove that the game remains PSPACE-complete even when every set has size 6.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Game
  • Maker-Breaker
  • Complexity
  • Reduction
  • PSPACE-complete
  • NL-hard


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