Undecidability in Finite Transducers, Defense Systems and Finite Substitutions

TL;DR

This paper proves that determining the equivalence of finite substitutions on a specific regular language is undecidable, building on previous foundational work in the field.

Contribution

It provides a detailed proof establishing the undecidability of finite substitution equivalence, extending prior theoretical results.

Findings

Proof of undecidability for finite substitution equivalence

Extension of Lisovik's work on related problems

Clarification of limits in automata and formal language decision procedures

Abstract

In this manuscript we present a detailed proof for undecidability of the equivalence of finite substitutions on regular language $b\{0,1\}^*c$. The proof is based on the works of Leonid P. Lisovik.