On Logic Gates with Complex Numbers

TL;DR

This paper explores a novel formalism for logic gates using complex differential operators and holomorphic functions, establishing a connection between oscillatory behavior and computational logic, with implications for various computing systems.

Contribution

It introduces a new approach to modeling logic gates with complex numbers and demonstrates the formalism's universality across different computing paradigms.

Findings

Complex differential operators can represent logic gates.

Oscillatory behavior relates to logical operations.

Formalism is applicable to diverse computing systems.

Abstract

Logic gates can be written in terms of complex differential operators, where the inputs and outputs are holomorphic functions with several variables. Using the polar representation of complex numbers, we arrive at an immediate connection between the oscillatory behavior of the system and logic gates. We discuss the universality of this formalism in a variety of computing systems.