Mean-Payoff Games and Propositional Proofs

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


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.


Proof System Interpolation Problem Boolean Variable Boolean Formula Positional Strategy 
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© 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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