Abstract
A simple, and easy-to-check, property of a symmetric boolean function is shown to imply a 4n-O(1) lower bound on the circuit complexity of the function over U2 = B2 - {⊗, ≡}, the basis of unate dyadic boolean functions. Among the functions to which this lower bound applies are the modular functions MODk (n) for any fixed k ≥ 3 (MODk (n) is the function which returns 1 if and only if (Σ xi) mod k = O). Finally, a 5n upper bound is obtained on the circuit complexity over U2 of the function MOD4 (n).
Original language | English |
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Pages (from-to) | 499-505 |
Number of pages | 7 |
Journal | SIAM Journal on Computing |
Volume | 20 |
Issue number | 3 |
DOIs | |
State | Published - 1991 |