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doi:10.1016/0304-3975(96)00007-2 
Copyright © 1996 Published by Elsevier Science B.V.
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On a small class of Boolean sums
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Tatsuie Tsukiji
Communicated by M.S. Paterson
Available online 20 February 1999.
Abstract
In this paper, we prove that almost all members of a certain natural class of n-input, n-output Boolean sums of cardinality 2n have monotone circuit complexity n2/2O((log log n)2). As a corollary, it is shown that there is a linear space computable Boolean sum whose monotone complexity is n2/2O((log log n)2) The main combinatorial achievement in the paper is as follows. For a subset D of [n],1 denote by s(D) the largest integer k such that EA, B
A = B = k & A + B 
D. We prove that s(D) = 2O((log log n)2) for almost all D.
Article Outline
1 We use [n] to denote the set 0,…,n - 1.
