Boolean Algebraic Programs as a Methodology for Symbolically Demonstrating Lower and Upper Bounds of Algorithms and Determinism

TL;DR

This paper introduces a Boolean Algebraic Programming methodology for symbolically analyzing algorithms to determine their lower and upper bounds, providing a new approach to evaluating computational complexity and determinism.

Contribution

It presents a novel Boolean algebraic programming approach for symbolic analysis of algorithms' bounds and determinism, enabling direct proof of complexity.

Findings

Successfully analyzed an example problem using the method

Proved bounds and determinism through Boolean algebraic programming

Demonstrated the method's effectiveness in complexity analysis

Abstract

The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic manipulation of Machines, Functions, and Inputs is presented which allows for direct analysis of time complexities and proof of deterministic methodologies. It is demonstrated through the analysis of a particular problem which is proven and solved through the application of Boolean algebraic programming.