A Class of Boolean Functions with Linear Combinatorial Complexity
Name
MIT-LCS-TM-055.pdf
Size
5.16 MB
Format
Adobe PDF
Checksum (MD5)
b51f5ef42a37181f8d919f65c9a8c026
Author(s)
Hsieh, W. N.
Harper, L.H.
Savage, J.E.
Date Issued
October 1974
Series/Report no.
MIT-LCS-TM-055
MAC-TM-055
Abstract
In this paper we investigate the combinatorial complexity of Boolean functions satisfying a certain property, P^nk,m. A function of n variable has the P^nk,m property if there are at least m functions obtainable from each way of restricting it to a subset of n-l variables. We show that the complexity of P^n3,5 function is no less than 7n-4/6, and this bound cannot be much improved. Further, we find that for each k, there are p^k,2^k functions with complexity linear in n.
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