Circuit Lower Bounds à la Kolmogorov

Abstract In a recent paper, Razborov ( in "Feasible Mathematics II" (P. Clote and J. Remmel, Eds.), gave a new combinatorial proof of Hastad′s switching lemma ( in "Randomness and Computation" (S. Micali, Ed.), pp. 143-170, 1989) eliminating the probabilistic argument altogether. In this paper we adapt his proof and propose a Kolmogorov complexity-style switching lemma, from which we derive the probabilistic switching lemma as well as a Kolmogorov complexity-style proof of circuit lower bounds for parity.

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