DNF complexity of complete boolean functions
Yura Maximov
TL;DR
This paper investigates the DNF complexity of complete boolean functions that are mostly 1, providing tight bounds based on literals and conjunctions, using hypercube covering approximations.
Contribution
It introduces a novel approach to analyze DNF complexity of functions with sparse zeroes, deriving tight bounds through hypercube covering methods.
Findings
Established tight bounds on DNF complexity for complete functions.
Developed an efficient approximation method for hypercube covering related to DNF.
Analyzed the complexity in terms of literals and conjunctions.
Abstract
In this paper we analyse the complexity of boolean functions takes value 0 on a sufficiently small number of points. For many functions this leads to the analysis of a single function attains 0 only on unsigned representation of numbers from 1 to d for various d. Here we obtain a tight bounds on the DNF complexity of complete functions in terms of the number of literals and conjunctions. The method is based on a certain efficient approximation of the hypercube covering problem related to DNF complexity of a given boolean function.
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Coding theory and cryptography · Formal Methods in Verification