Summary
In this paper we investigate the method of Nechiporuk [3] for deriving lower bounds on the formula size of Boolean functions. At first we prove non-linear lower bounds for functions which are related to the existence of a k-clique or a k-circle in a graph. Furthermore we determine the formula size of the “disjoint disjunction” of the outputs of the Boolean matrix product. Finally we show how useful the method may be in the case of monotone functions if the length of the prime implicants is bounded.
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Schürfeld, U. New lower bounds on the formula size of Boolean functions. Acta Informatica 19, 183–194 (1983). https://doi.org/10.1007/BF00264475
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DOI: https://doi.org/10.1007/BF00264475