@MISC{Pudlák01monotonecomplexity, author = {Pavel Pudlák}, title = {Monotone Complexity and the Rank of Matrices}, year = {2001} }

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Abstract

blem, because what is computed in the game is not a function, but only a relation. On the other hand, computing the (two party) communication complexity of a function is usually not dicult, thus the task of proving lower bounds can be considerably simplied, if one could replace the relation in the KW game by a function. 1 Let us consider the case of monotone circuit depth. The KW game for a monotone function f is dened as follows. One player gets a minterm of f , the other gets a maxterm of f . Think of the min- and maxterms as subsets of [n]. The goal of the players is to nd an i 2 [n] in the intersection of the given minterm and the given maxterm. In general we know that each minterm intersects each maxterm, but there may be more than one element in the intersection. To require that the intersection be of size one is too restrictive. We do not know whether under this re