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Mean-Payoff Games and Propositional Proofs

  • Albert Atserias
  • Elitza Maneva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6198)

Abstract

We associate a CNF-formula to every instance of the mean-payoff game problem in such a way that if the value of the game is non-negative the formula is satisfiable, and if the value of the game is negative the formula has a polynomial-size refutation in Σ2-Frege (a.k.a. DNF-resolution). This reduces the problem of solving mean-payoff games to the weak automatizability of Σ2-Frege, and to the interpolation problem for Σ2,2-Frege. Since the interpolation problem for Σ1-Frege (i.e. resolution) is solvable in polynomial time, our result is close to optimal up to the computational complexity of solving mean-payoff games. The proof of the main result requires building low-depth formulas that compute the bits of the sum of a constant number of integers in binary notation, and low-complexity proofs of their relevant arithmetic properties.

Keywords

Proof System Interpolation Problem Boolean Variable Boolean Formula Positional Strategy 
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 2010

Authors and Affiliations

  • Albert Atserias
    • 1
  • Elitza Maneva
    • 2
  1. 1.Universitat Politècnica de Catalunya 
  2. 2.Universitat de Barcelona 

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