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 \(\mathsf {GI}\), the complexity class of graph isomorphism, and that the existence problems of block maps, factor maps and embeddings are \(\mathsf {NP}\)-complete.
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Notes
- 1.
There is a common period \(p \in \mathbb {N}\) for the configurations in \(Y\), and if this period breaks infinitely many times in the right tail of \(x\), then \(X_i^R\) is not contained in \(Y\).
- 2.
From Proposition 2, one can extract that in the rank \(1\) case, conjugacy of edge shifts is equivalent to the graphs defining them being isomorphic.
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Salo, V., Törmä, I. (2015). Complexity of Conjugacy, Factoring and Embedding for Countable Sofic Shifts of Rank 2. In: Isokawa, T., Imai, K., Matsui, N., Peper, F., Umeo, H. (eds) Cellular Automata and Discrete Complex Systems. AUTOMATA 2014. Lecture Notes in Computer Science(), vol 8996. Springer, Cham. https://doi.org/10.1007/978-3-319-18812-6_10
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