Decidability of Existence and Construction of a Complement of a given Function

TL;DR

This paper explores the theoretical conditions under which a complement of a given function exists and provides algorithms for constructing such a complement.

Contribution

It introduces a formal definition of function complements, establishes conditions for their existence, and offers algorithms for their construction.

Findings

Conditions for the existence of a function's complement are established.

Algorithms for constructing a complement are proposed.

Theoretical framework for function complementarity is developed.

Abstract

This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.