Threefold Post Correspondence System

TL;DR

This paper introduces the threefold Post correspondence system (3PCS), a new computational model, and explores its relation to the classical Post correspondence problem, proposing a conjecture about its decidability.

Contribution

It defines the 3PCS model, links it to multiple instances of the Post correspondence problem, and conjectures about its decidability, advancing theoretical understanding.

Findings

Definition of 3PCS as a new computational model

Association of 3PCS with three Post correspondence systems

Conjecture on the decidability of 3PCS and related problems

Abstract

We introduce the concept of a threefold Post correspondence system (3PCS for short) and we consider it as an instance of the threefold Post correspondence problem. With each 3PCS, we associate three Post correspondence systems, i.e., three instances of the Post correspondence problem. We conjecture that for each 3PCS, the question of the threefold Post correspondence problem or for some associated Post correspondence system the question of the Post correspondence problem is decidable.