# On Derivatives and Subpattern Orders of Countable Subshifts

@inproceedings{Salo2012OnDA, title={On Derivatives and Subpattern Orders of Countable Subshifts}, author={Ville Salo and Ilkka T{\"o}rm{\"a}}, booktitle={AUTOMATA \& JAC}, year={2012} }

We study the computational and structural aspects of countable two-dimensional SFTs and other subshifts. Our main focus is on the topological derivatives and subpattern posets of these objects, and our main results are constructions of two-dimensional countable subshifts with interesting properties. We present an SFT whose iterated derivatives are maximally complex from the computational point of view, a sofic shift whose subpattern poset contains an infinite descending chain, a family of SFTs…

## 2 Citations

### 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…

### Structuring multi-dimensional subshifts

- MathematicsArXiv
- 2013

The simplest aperiodic configurations in countable SFTs are characterized, a combinatorial characterization of uncountable subshifts is given, and it is proved that some Cantor-Bendixson ranks are impossible for countableSFTs.

## References

SHOWING 1-10 OF 19 REFERENCES

### Effective closed subshifts in 1D can be implemented in 2D

- MathematicsFields of Logic and Computation
- 2010

This paper shows that every one-dimensional effectively closed subshift can be implemented by a local rule in two dimensions and uses the fixed-point construction of an aperiodic tile set and its extensions.

### Endomorphisms and automorphisms of the shift dynamical system

- MathematicsMathematical systems theory
- 2005

It is shown that closed subset of X(SQ which is invariant under a defines a subdynamical system, and that these mappings, composed with powers of the shift, constitute the entire class of continuous transformations which commute with the shift.

### Undecidability and nonperiodicity for tilings of the plane

- Mathematics
- 1971

This paper is related to the work of Hao Wang and others growing out of a problem which he proposed in [8], w 4.1. Suppose that we are given a finite set of unit squares with colored edges, placed…

### P01\it \Pi^0_1 Sets and Tilings

- MathematicsTAMC
- 2011

In this paper, we prove that given any \(\it \Pi^0_1\) subset P of {0,1}ℕ there is a tileset τ with a countable set of configurations C such that P is recursively homeomorphic to C ∖ U where U is a…

### The undecidability of the domino problem

- Medicine
- 1966

A way to break the boredom in reading is choosing undecidability of the domino problem as the reading material.

### An Introduction to Symbolic Dynamics and Coding

- Mathematics
- 1995

Requiring only a undergraduate knowledge of linear algebra, this first general textbook includes over 500 exercises that explore symbolic dynamics as a method to study general dynamical systems.

### Structural aspects of tilings

- Computer ScienceSTACS
- 2008

It is shown that a tile-set that produces only periodic tilings produces only a finite number of them, and it is proved that the uncountable case may have a completely different structure.