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

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 3-by-3 integer matrix semigroups works for the symmetric PCP, but not for the PCP in general.Comment: 12 pages. Small corrections and clarifications were added in version