4n lower bound on the combinational complexity of certain symmetric boolean functions over the basis of unate dyadic boolean functions

Uri Zwick*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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 languageEnglish
Pages (from-to)499-505
Number of pages7
JournalSIAM Journal on Computing
Volume20
Issue number3
DOIs
StatePublished - 1991

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