# Computational Aspects of Cellular Automata on Countable Sofic Shifts

@inproceedings{Salo2012ComputationalAO, title={Computational Aspects of Cellular Automata on Countable Sofic Shifts}, author={Ville Salo and Ilkka T{\"o}rm{\"a}}, booktitle={MFCS}, year={2012} }

We investigate the computational properties of cellular automata on countable (equivalently, zero entropy) sofic shifts with an emphasis on nilpotency, periodicity, and asymptotic behavior. As a tool for proving decidability results, we prove the Starfleet Lemma, which is of independent interest. We present computational results including the decidability of nilpotency and periodicity, the undecidability of stability of the limit set, and the existence of a $\mathrm{\Pi}^0_1$-complete limit set…

## 11 Citations

### Strict Asymptotic Nilpotency in Cellular Automata

- MathematicsAUTOMATA
- 2017

The problem of which subshifts support strictly asymptotically nilpotent CA, that is, asymptonically nilpotsent CA which are not nil Potent, is discussed in some detail.

### Groups and Monoids of Cellular Automata

- MathematicsAutomata
- 2015

Groups and monoids defined by cellular automata on full shifts, sofic shifts, minimal subsh shifts, countable subshifts and coded and synchronized systems are discussed.

### Hard Asymptotic Sets for One-Dimensional Cellular Automata

- Mathematics, Computer ScienceArXiv
- 2013

We prove that the (language of the) asymptotic set (and the nonwandering set) of a one-dimensional cellular automaton can be $\SIGMA^1_1$-hard. We do not go into much detail, since the constructions…

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

- MathematicsAutomata
- 2014

It is proved 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 \(NP}\)-complete.

### Subshifts with sparse traces Ville Salo

- Mathematics
- 2019

We study two-dimensional subshifts whose horizontal trace (a.k.a. projective subdynamics) contains only points of finite support. Our main result is a classification result for such subshifts…

### Subshifts with sparse traces

- MathematicsStudia Mathematica
- 2020

We study two-dimensional subshifts whose horizontal trace (a.k.a. projective subdynamics) contains only points of finite support. Our main result is a classification result for such subshifts…

### Constructions with Countable Subshifts of Finite Type

- MathematicsFundam. Informaticae
- 2013

We present constructions of countable two-dimensional subshifts of finite type SFTs with interesting properties. Our main focus is on properties of the topological derivatives and subpattern posets…

### Distortion element in the automorphism group of a full shift

- MathematicsArXiv
- 2022

We show that there is a distortion element in a finitely-generated subgroup G of the automorphism group of the full shift, namely an element of infinite order whose word norm grows…

### A note on subgroups of automorphism groups of full shifts

- MathematicsErgodic Theory and Dynamical Systems
- 2016

We discuss the set of subgroups of the automorphism group of a full shift and submonoids of its endomorphism monoid. We prove closure under direct products in the monoid case and free products in the…

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