293 research outputs found

    nested PLS

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    In this note we will introduce a class of search problems, called nested Polynomial Local Search (nPLS) problems, and show that definable NP search problems, i.e., Σ1b\Sigma^b_1-definable functions in T22T^2_2 are characterized in terms of the nested PLS

    Random Resolution Refutations

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    We study the random resolution refutation system definedin [Buss et al. 2014]. This attempts to capture the notion of a resolution refutation that may make mistakes but is correct most of the time. By proving the equivalence of several different definitions, we show that this concept is robust. On the other hand, if P does not equal NP, then random resolution cannot be polynomially simulated by any proof system in which correctness of proofs is checkable in polynomial time. We prove several upper and lower bounds on the width and size of random resolution refutations of explicit and random unsatisfiable CNF formulas. Our main result is a separation between polylogarithmic width random resolution and quasipolynomial size resolution, which solves the problem stated in [Buss et al. 2014]. We also prove exponential size lower bounds on random resolution refutations of the pigeonhole principle CNFs, and of a family of CNFs which have polynomial size refutations in constant depth Frege

    Mathematical Logic: Proof Theory, Constructive Mathematics

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    [no abstract available

    The Arity Hierarchy in the Polyadic μ\mu-Calculus

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    The polyadic mu-calculus is a modal fixpoint logic whose formulas define relations of nodes rather than just sets in labelled transition systems. It can express exactly the polynomial-time computable and bisimulation-invariant queries on finite graphs. In this paper we show a hierarchy result with respect to expressive power inside the polyadic mu-calculus: for every level of fixpoint alternation, greater arity of relations gives rise to higher expressive power. The proof uses a diagonalisation argument.Comment: In Proceedings FICS 2015, arXiv:1509.0282
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