Binary (generalized) Post Correspondence Problem

An instance of the (Generalized) Post Correspondence Problem is during the decision process typically reduced to one or more other instances, called its successors. In this paper we study the reduction tree of GPCP in the binary case. This entails in particular a detailed analysis of the structure of end blocks. We give an upper bound for the number of end blocks, and show that even if an instance has more than one successor, it can nevertheless be reduced to a single instance. This, in particular, implies that binary GPCP can be decided in polynomial time. The Post Correspondence Problem, PCP for short, is one of the most important undecidable problems in the theory of computation. The PCP has been very useful in proving undecidability results in automata and formal language theory, in matrix theory etc. The PCP was proved undecidable by E. Post in 1946, see [14], in the following form: given two lists of words (u1, u2, . . . , un) and (v1, v2, . . . , vn), the task is to determine w...

• Type: Journal
• Year: 2002
• Where: TCS
• Authors: Vesa Halava, Tero Harju, Mika Hirvensalo
• Keywords: Important Undecidable Problems, Post Correspondence Problem, TCS 2002, Theoretical Computer Science, Theory