Classes of states of discrete systems

TL;DR

This paper introduces a symmetry-based method to reduce the complexity of simulating discrete systems by grouping states into classes, applicable to various graph types and system configurations.

Contribution

It presents a novel approach for state reduction in discrete systems using symmetry, applicable to directed, undirected, weighted, and unweighted graphs.

Findings

Effective reduction of system size through state classes.

Applicable to diverse graph types and system configurations.

Demonstrated usefulness in multiple system applications.

Abstract

We present a method which allows reduction of a size of a simulated system. The method can be applied to any system where one can define a finite set of possible states of the system and an elementary process which transforms one state of the system to another. The method is based on the symmetry of the system symmetry; we get classes of states, which can be used instead of states. We present a detailed procedure for undirected/directed and/or unweighted/weighted graphs. We show applications of the method for different types of systems.