The symmetric Post Correspondence Problem, and errata for the freeness problem for matrix semigroups

Abstract

In this paper, we define the symmetric Post Correspondence Problem (PCP) and prove that it is undecidable. As an application, we show that the original proof of undecidability of the freeness problem for [Formula: see text] integer matrix semigroups works for the symmetric PCP, but not for the PCP in general.