Determinism in Multi-Soliton Automata

TL;DR

This paper explores various concepts of determinism in multi-soliton automata, analyzing their complexity and introducing the concept of perfect determinism as an extension of strong determinism.

Contribution

It extends the study of determinism from single to multi-soliton automata, characterizes strongly deterministic automata, and introduces perfect determinism.

Findings

Degree of non-determinism correlates with descriptional complexity.

Characterization of strongly deterministic multi-soliton automata.

Introduction of the concept of perfect determinism.

Abstract

Soliton automata are mathematical models of soliton switching in chemical molecules. Several concepts of determinism for soliton automata have been defined. The concept of strong determinism has been investigated for the case in which only a single soliton can be present in a molecule. In the present paper, several different concepts of determinism are explored for the multi-soliton case. It is shown that the degree of non-determinism is a connected measure of descriptional complexity for multi-soliton automata. A characterization of the class of strongly deterministic multi-soliton automata is presented. Finally, the concept of perfect determinism, forming a natural extension of strong determinism, is introduced and considered for multi-soliton automata.