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

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.Comment: 14 pages, 1 figure. to appear in the postceedings of AUTOMATA 2014, published by Springe

Decidability and Universality of Quasiminimal Subshifts

We introduce the quasiminimal subshifts, subshifts having only finitely many subsystems. With $\mathbb{N}$-actions, their theory essentially reduces to the theory of minimal systems, but with $\mathbb{Z}$-actions, the class is much larger. We show many examples of such subshifts, and in particular construct a universal system with only a single proper subsystem, refuting a conjecture of [Delvenne, K\r{u}rka, Blondel, '05].Comment: 40 pages, 1 figure, submitted to JCS