Complexity of Conjugacy, Factoring and Embedding for Countable Sofic Shifts of Rank 2

TL;DR

This paper investigates the computational complexity of various problems related to countable sofic shifts of rank 2, establishing their conjugacy problem as graph isomorphism complete and related existence problems as NP-complete.

Contribution

It proves that conjugacy for these shifts is GI-complete and that block map, factor map, and embedding existence problems are NP-complete, advancing understanding of their computational complexity.

Findings

Conjugacy problem is GI-complete.

Existence of block maps, factor maps, and embeddings are NP-complete.

Results apply to countable sofic shifts of Cantor-Bendixson rank at most 2.

Abstract

In this article, we study countable sofic shifts of Cantor-Bendixson rank at most 2. We prove that their conjugacy problem is complete for GI, the complexity class of graph isomorphism, and that the existence problems of block maps, factor maps and embeddings are NP-complete.