Abstract
We show that the shrinkage exponent, under random restrictions, of formulae over a finite complete basis B of Boolean functions, is strictly greater than 1 if and only if all the functions in B are unate, i.e., monotone increasing or decreasing in each of their variables. As a consequence, we get non-linear lower bounds on the formula complexity of the parity function over any basis composed only of unate functions.
Original language | English |
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Pages (from-to) | 28-40 |
Number of pages | 13 |
Journal | COMPUTATIONAL COMPLEXITY |
Volume | 10 |
Issue number | 1 |
Publication status | Published - 2001 |