TCS 2014: Theoretical Computer Science pp 104-110 | Cite as
Sensitivity, Block Sensitivity, and Certificate Complexity of Unate Functions and Read-Once Functions
Conference paper
Abstract
Sensitivity, block sensitivity, and certificate complexity are complexity measures for Boolean functions. In this paper, we prove that these three complexity measures are equal to each other if a Boolean function is a unate function or a read-once function. We also prove \(\sqrt{n}\) tight lower bounds for the three complexity measures of read-once functions. As an application of our results, the decision tree complexity of unate functions and read-once functions is upper bounded by the square of the sensitivity of the function.
Keywords
Boolean Function Unate Function Monotone Function Complexity Measure Boolean Formula
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