Assisted Problem Solving and Decompositions of Finite Automata

TL;DR

This paper explores new types of decompositions of deterministic finite automata, revealing a spectrum of languages with varying degrees of decomposability, from undecomposable to perfectly decomposable.

Contribution

It introduces a formal framework for assisted problem solving through automata decompositions and uncovers a diverse landscape of decomposability types.

Findings

Existence of languages with various degrees of decomposability

Introduction of new automata decomposition types

Framework for assisted problem solving using automata

Abstract

A study of assisted problem solving formalized via decompositions of deterministic finite automata is initiated. The landscape of new types of decompositions of finite automata this study uncovered is presented. Languages with various degrees of decomposability between undecomposable and perfectly decomposable are shown to exist.