Remarks on Jurdzinski and Lorys' proof that palindromes are not a Church-Rosser language

TL;DR

This paper discusses proofs that certain language classes, including palindromes and non-square bitstrings, are not Church-Rosser, providing simplified and alternative proofs using Turing machines and automata theory.

Contribution

It offers a reformulation of Jurdzinski and Lorys' proof using Turing machines and presents an alternative proof for non-square bitstrings not being Church-Rosser.

Findings

Palindromes are not a Church-Rosser language.

Non-square bitstrings, a context-free set, are not Church-Rosser.

Simplified proof techniques using Turing machines are introduced.

Abstract

In 2002 Jurdzinski and Lorys settled a long-standing conjecture that palindromes are not a Church-Rosser language. Their proof required a sophisticated theory about computation graphs of 2-stack automata. We present their proof in terms of 1-tape Turing machines.We also provide an alternative proof of Buntrock and Otto's result that the set of non-square bitstrings, which is context-free, is not Church-Rosser.