9 found
  1.  6
    An exponential separation between the parity principle and the pigeonhole principle.Paul Beame & Toniann Pitassi - 1996 - Annals of Pure and Applied Logic 80 (3):195-228.
    The combinatorial parity principle states that there is no perfect matching on an odd number of vertices. This principle generalizes the pigeonhole principle, which states that for a fixed bipartition of the vertices, there is no perfect matching between them. Therefore, it follows from recent lower bounds for the pigeonhole principle that the parity principle requires exponential-size bounded-depth Frege proofs. Ajtai previously showed that the parity principle does not have polynomial-size bounded-depth Frege proofs even with the pigeonhole principle as an (...)
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  2.  47
    Lower Bounds for cutting planes proofs with small coefficients.Maria Bonet, Toniann Pitassi & Ran Raz - 1997 - Journal of Symbolic Logic 62 (3):708-728.
    We consider small-weight Cutting Planes (CP * ) proofs; that is, Cutting Planes (CP) proofs with coefficients up to $\operatorname{Poly}(n)$ . We use the well known lower bounds for monotone complexity to prove an exponential lower bound for the length of CP * proofs, for a family of tautologies based on the clique function. Because Resolution is a special case of small-weight CP, our method also gives a new and simpler exponential lower bound for Resolution. We also prove the following (...)
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  3. Minimum propositional proof length is NP-Hard to linearly approximate.Michael Alekhnovich, Sam Buss, Shlomo Moran & Toniann Pitassi - 2001 - Journal of Symbolic Logic 66 (1):171-191.
    We prove that the problem of determining the minimum propositional proof length is NP- hard to approximate within a factor of 2 log 1 - o(1) n . These results are very robust in that they hold for almost all natural proof systems, including: Frege systems, extended Frege systems, resolution, Horn resolution, the polynomial calculus, the sequent calculus, the cut-free sequent calculus, as well as the polynomial calculus. Our hardness of approximation results usually apply to proof length measured either by (...)
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  4.  25
    University of Azores, Ponta Delgada, Azores, Portugal June 30–July 4, 2010.Eric Allender, José L. Balcázar, Shafi Goldwasser, Denis Hirschfeldt, Sara Negri, Toniann Pitassi & Ronald de Wolf - 2011 - Bulletin of Symbolic Logic 17 (3).
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  5. An exponential separation between the matching principles and the pigeonhole principle, forthcoming.Paul Beame & Toniann Pitassi - forthcoming - Annals of Pure and Applied Logic.
  6.  36
    Madison, WI, USA March 31–April 3, 2012.Alan Dow, Isaac Goldbring, Warren Goldfarb, Joseph Miller, Toniann Pitassi, Antonio Montalbán, Grigor Sargsyan, Sergei Starchenko & Moshe Vardi - 2013 - Bulletin of Symbolic Logic 19 (2).
  7.  48
    The Complexity of Resolution Refinements.Joshua Buresh-Oppenheim & Toniann Pitassi - 2007 - Journal of Symbolic Logic 72 (4):1336 - 1352.
    Resolution is the most widely studied approach to propositional theorem proving. In developing efficient resolution-based algorithms, dozens of variants and refinements of resolution have been studied from both the empirical and analytic sides. The most prominent of these refinements are: DP (ordered). DLL (tree), semantic, negative, linear and regular resolution. In this paper, we characterize and study these six refinements of resolution. We give a nearly complete characterization of the relative complexities of all six refinements. While many of the important (...)
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  8.  14
    University of California, San Diego, March 20–23, 1999.Julia F. Knight, Steffen Lempp, Toniann Pitassi, Hans Schoutens, Simon Thomas, Victor Vianu & Jindrich Zapletal - 1999 - Bulletin of Symbolic Logic 5 (3).
  9.  65
    The Complexity of Analytic Tableaux.Noriko H. Arai, Toniann Pitassi & Alasdair Urquhart - 2006 - Journal of Symbolic Logic 71 (3):777 - 790.
    The method of analytic tableaux is employed in many introductory texts and has also been used quite extensively as a basis for automated theorem proving. In this paper, we discuss the complexity of the system as a method for refuting contradictory sets of clauses, and resolve several open questions. We discuss the three forms of analytic tableaux: clausal tableaux, generalized clausal tableaux, and binary tableaux. We resolve the relative complexity of these three forms of tableaux proofs and also resolve the (...)
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