Computational Understanding and Manipulation of Symmetries

TL;DR

This paper presents an algebraic approach to understanding and manipulating symmetries in systems, exemplified through permutation puzzles, enabling structural insights without the need for learning.

Contribution

It introduces an algebraic coordinatization method for symmetry analysis, providing structural understanding beyond just solving puzzles.

Findings

Algebraic coordinatization effectively captures symmetry structures.

Method applies to permutation puzzles for structural insights.

Enables manipulation of symmetries without learning-based approaches.

Abstract

For natural and artificial systems with some symmetry structure, computational understanding and manipulation can be achieved without learning by exploiting the algebraic structure. Here we describe this algebraic coordinatization method and apply it to permutation puzzles. Coordinatization yields a structural understanding, not just solutions for the puzzles.