Average case complexity of DNFs and Shannon semi-effect for narrow subclasses of boolean functions

TL;DR

This paper investigates the average case complexity of DNF representations for narrow subclasses of boolean functions, linking complexity bounds to Shannon effects and semi-effects through reductions to set covering problems.

Contribution

It introduces new bounds on DNF complexity for narrow boolean functions by reducing the problem to set covering, highlighting connections with Shannon effects.

Findings

Bounds on DNF complexity for narrow subclasses

Reduction of complexity analysis to set covering problems

Insights into Shannon semi-effect for these classes

Abstract

In this paper we establish some bounds on the complexity of disjunctive normal forms of boolean function from narrow subclasses (e.g. functions takes value 0 in a limited number of points). The bounds are obtained by reduction the initial problem to a simple set covering problem. The nature of the complexity bounds provided is tightly connected with Shannon effect and semi-effect for this classes.