Improving problem solving by exploiting the concept of symmetry

TL;DR

This paper explores how the concept of symmetry can be leveraged to enhance problem-solving processes by providing precise definitions and illustrating how symmetry can be exploited to improve search efficiency.

Contribution

It introduces a formal framework for defining problems and solutions and demonstrates how symmetry can be utilized to optimize problem-solving strategies.

Findings

Defined problem and solution elements with examples

Constructed search processes based on problem definitions

Proposed methods to exploit symmetry for improved problem solving

Abstract

We investigate the concept of symmetry and its role in problem solving. This paper first defines precisely the elements that constitute a "problem" and its "solution," and gives several examples to illustrate these definitions. Given precise definitions of problems, it is relatively straightforward to construct a search process for finding solutions. Finally this paper attempts to exploit the concept of symmetry in improving problem solving.