Some New Results on Post Correspondence Problem and Its Modifications
In this work we shall consider some new result on the famous word problem called the Post Correspondence Problem (PCP), initially defined by E. Post. Halava, Hirvensalo and de Wolf [4] proved that the PCP is decidable if we assume that the morphisms are marked. Moreover, Halava, Harju and Hirvensalo [2] proved that even the generalized PCP is decidable in the case of marked morphisms. As a corollary a new shorter proof was achieved for the PCP in the binary case. Here we shall consider the ideas behind these proofs. We also present a proof for the undecidability of the PCP in the case where the morphisms are permutations of each others.