On the Steps of Emil Post: from Normal Systems to the Correspondence Decision Problem

Abstract

In 1946 Emil Leon Post (Bull. Amer. Math. Soc. 52 (1946), 264-268) introduced his famous correspondence decision problem, nowadays known as the Post Correspondence Problem (PCP). Post proved the undecidability of the PCP by a reduction from his normal systems. In the present article we follow the steps of Post, and give another, somewhat simpler and more straightforward proof of the undecidability of the problem by using the same source of reductions as Post did. We investigate these, very different, techniques, and point out out some peculiarities in the approach taken by Post.