Abstract
AbstractBoolean functions have important applications in molecular regulatory networks, engineering, cryptography, information technology, and computer science. Symmetric Boolean functions have received a lot of attention in several decades. Sensitivity and block sensitivity are important complexity measures of Boolean functions. In this paper, we study the sensitivity of elementary symmetric Boolean functions and obtain many explicit formulas. We also obtain a formula for the block sensitivity of symmetric Boolean functions and discuss its applications in elementary symmetric Boolean functions.
Highlights
In 1938, Shannon [28] recognized that symmetric functions had efficient switch network implementation
We prove a formula for the block sensitivity of symmetric Boolean functions. This is the first study about the block sensitivity of symmetric Boolean functions. We apply this formula to elementary symmetric Boolean functions and show that the block sensitivity can be strictly greater than the sensitivity for some elementary symmetric Boolean functions
Based on the value vector of a symmetric Boolean function, we provide a formula for its j=0 block sensitivity
Summary
In 1938, Shannon [28] recognized that symmetric functions had efficient switch network implementation. [8], the authors studied the balancedness of elementary symmetric Boolean functions and they proposed a conjecture which has received a lot of attention [4,5,6,8, 9,13,14,31]. Sensitivities and block sensitivities of elementary symmetric Boolean functions 435. This is the first study about the block sensitivity of symmetric Boolean functions.
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