Short propositional refutations for dense random 3CNF formulas |
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Authors: | Sebastian Müller Iddo Tzameret |
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Institution: | 1. NII, National Institute of Informatics, Tokyo, Japan;2. Computer Science Department, Royal Holloway, University of London, United Kingdom |
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Abstract: | Random 3CNF formulas constitute an important distribution for measuring the average-case behavior of propositional proof systems. Lower bounds for random 3CNF refutations in many propositional proof systems are known. Most notable are the exponential-size resolution refutation lower bounds for random 3CNF formulas with Ω(n1.5−ε) clauses (Chvátal and Szemerédi 14], Ben-Sasson and Wigderson 10]). On the other hand, the only known non-trivial upper bound on the size of random 3CNF refutations in a non-abstract propositional proof system is for resolution with Ω(n2/log?n) clauses, shown by Beame et al. 6]. In this paper we show that already standard propositional proof systems, within the hierarchy of Frege proofs, admit short refutations for random 3CNF formulas, for sufficiently large clause-to-variable ratio. Specifically, we demonstrate polynomial-size propositional refutations whose lines are TC0 formulas (i.e., TC0-Frege proofs) for random 3CNF formulas with n variables and Ω(n1.4) clauses. |
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Keywords: | 68Q25 03F20 03F30 03D15 |
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