The complexity of mean payoff games on graphs
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Information and Computation - Special issue: logic and computational complexity
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SIAM Journal on Computing
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SIAM Journal on Computing
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Computational Complexity
Combinatorial structure and randomized subexponential algorithms for infinite games
Theoretical Computer Science
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LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
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SIAM Journal on Computing
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ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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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 @S"2-Frege (i.e. DNF-resolution). This reduces mean-payoff games to the weak automatizability of @S"2-Frege, and to the interpolation problem for @S"2","2-Frege. Since the interpolation problem for @S"1-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 the required arithmetic properties.