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Characterizing Propositional Proofs as Noncommutative Formulas

2018
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SIAM journal on computing (Print)
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Does every Boolean tautology have a short propositional-calculus proof? Here, a propositional-calculus (i.e., Frege) proof is any proof starting from a set of axioms and deriving new Boolean formulas using a fixed set of sound derivation rules. Establishing any superpolynomial size lower bound on Frege proofs (in terms of the size of the formula proved) is a major open problem in proof complexity, and among a handful of fundamental hardness questions in complexity theory by and large.

doi:10.1137/16m1107632
fatcat:wlvtdrtze5bmpbsc7l5qja7ua4