The complexity of Boolean functions
The complexity of Boolean functions
Sorting in c log n parallel steps
Combinatorica
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Algebraic proofs over noncommutative formulas
Information and Computation
Algebraic proofs over noncommutative formulas
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
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We show that an LK proof of size m of a monotone sequent (a sequent that contains only formulas in the basis ∧,∨) can be turned into a proof containing only monotone formulas of size mO(log m) and with the number of proof lines polynomial in m. Also we show that some interesting special cases, namely the functional and the onto versions of Pigeonhole Principle and a version of the Matching Principle, have polynomial size monotone proofs. We prove that LK is polynomially bounded if and only if its monotone fragment is.