A new lower bound on the monotone network complexity of Boolean sums
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Neciporuk , Lamagna/Savage  and Tarjan  determined the monotone network complexity of a set of Boolean sums if each two sums have at most one variable in common. By this result they could define explicitely a set of n Boolean sums which depend on n variables and whose monotone complexity is of order n3/2. In the main theorem of this paper we prove a more general lower bound on the monotone network complexity of Boolean sums. Our lower bound is for many Boolean sums the first nontrivial lower bound. On the other side we can prove that the best lower bound which the main theorem yields is the n3/2-bound cited above. For the proof we use the technical trick of assuming that certain functions are given for free.
KeywordsInformation System Operating System Data Structure Communication Network Information Theory
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