The simplified weighted sum function and its average sensitivity
Jiyou Li, Chu Luo
TL;DR
This paper introduces a simplified version of the weighted sum Boolean function, maintaining its key properties and sensitivity bounds, thereby making it easier to compute and analyze.
Contribution
The paper presents a simplified definition of the weighted sum Boolean function that preserves its essential properties and sensitivity bounds.
Findings
The simplified function retains the original sensitivity bounds.
The new definition is easier to compute and analyze.
Properties of the original function are preserved.
Abstract
In this paper we simplify the definition of the weighted sum Boolean function which used to be inconvenient to compute and use. We show that the new function has essentially the same properties as the previous one. In particular, the bound on the average sensitivity of the weighted sum Boolean function remains unchanged after the simplification.
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Advanced Combinatorial Mathematics · Advanced Algebra and Logic