Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts

05/10/2018
by   Julien Destombes, et al.
0

We propose necessary conditions of soficness of multidimensional shifts formulated in terms of resource-bounded Kolmogorov complexity. Using this technique we provide examples of effective and non-sofic shifts on Z^2 with very low block complexity: the number of admissible patterns of size n× n grows only as a polynomial in n.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/21/2023

Algorithmic complexity and soficness of shifts in dimension two

In this manuscript we study properties of multidimensional shifts. More ...
research
09/05/2019

Computational Complexity of k-Block Conjugacy

We consider several computational problems related to conjugacy between ...
research
02/05/2018

The expressiveness of quasiperiodic and minimal shifts of finite type

We study multidimensional minima and quasiperiodic shifts of finite type...
research
11/12/2008

Necessary Conditions for Discontinuities of Multidimensional Size Functions

Some new results about multidimensional Topological Persistence are pres...
research
06/01/2022

𝒮-adic characterization of minimal dendric shifts

Dendric shifts are defined by combinatorial restrictions of the extensio...
research
07/28/2022

Analysis and Computation of Multidimensional Linear Complexity of Periodic Arrays

Linear complexity is an important parameter for arrays that are used in ...
research
01/09/2022

Locality-Preserving Hashing for Shifts with Connections to Cryptography

Can we sense our location in an unfamiliar environment by taking a subli...

Please sign up or login with your details

Forgot password? Click here to reset