Another proof of undecidability for the correspondence decision problem - Had I been Emil Post

TL;DR

This paper provides a new, simpler proof of the undecidability of the Post Correspondence Problem by following Post's original reduction from Post Normal Systems, offering clearer insights into its computational limits.

Contribution

It introduces a more straightforward proof of undecidability for the Post Correspondence Problem using the same reduction source as Post's original work.

Findings

Confirmed the undecidability of the Post Correspondence Problem

Presented a simplified proof approach

Reinforced the foundational understanding of computational undecidability

Abstract

In 1946 Emil Leon Post (Bulletin of Amer. Math. Soc. 52 (1946), 264 - 268) defined a famous correspondence decision problem which is nowadays called the Post Correspondence Problem, and he proved that the problem is undecidable. In this article we follow the steps of Post, and give another, simpler and more straightforward proof of the undecidability of the problem using the same source of reduction as Post original did, namely, the Post Normal Systems.