Parity Games and Propositional Proofs

  • Arnold Beckmann
  • Pavel Pudlák
  • Neil Thapen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8087)


A propositional proof system is weakly automatizable if there is a polynomial time algorithm which separates satisfiable formulas from formulas which have a short refutation in the system, with respect to a given length bound. We show that if the resolution proof system is weakly automatizable, then parity games can be decided in polynomial time. We also define a combinatorial game and prove that resolution is weakly automatizable if and only if one can separate, by a set decidable in polynomial time, the games in which the first player has a positional winning strategy from the games in which the second player has a positional winning strategy.


Polynomial Time Algorithm Proof System Outgoing Edge Winning Strategy Propositional Formula 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Arnold Beckmann
    • 1
  • Pavel Pudlák
    • 2
  • Neil Thapen
    • 2
  1. 1.Department of Computer Science, College of ScienceSwansea UniversitySwanseaUK
  2. 2.Institute of Mathematics, Academy of Sciences of the Czech RepublicPraha 1Czech Republic

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