Evolution Theory of Self-Evolving Autonomous Problem Solving Systems

TL;DR

This paper develops a mathematical framework for self-evolving autonomous problem solving systems, focusing on abstraction, net transformations, and the evolution of solution spaces through algebraic and homomorphic methods.

Contribution

It introduces a novel formal model for self-evolution in autonomous problem solving, utilizing net homomorphisms, abstraction relations, and algebraic structures to analyze system decidability and evolution.

Findings

Established a new abstraction relation among nets.

Formulated a net block renetting system related to normal forms.

Defined a structure for self-evolving problem solving via algebraic saturation.

Abstract

The present study gives a mathematical framework for self-evolution within autonomous problem solving systems. Special attention is set on universal abstraction, thereof generation by net block homomorphism, consequently multiple order solving systems and the overall decidability of the set of the solutions. By overlapping presentation of nets new abstraction relation among nets is formulated alongside with consequent alphabetical net block renetting system proportional to normal forms of renetting systems regarding the operational power. A new structure in self-evolving problem solving is established via saturation by groups of equivalence relations and iterative closures of generated quotient transducer algebras over the whole evolution.