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

Abstract

We suggest necessary conditions of soficness of multidimensional shifts formulated in termsof resource-bounded Kolmogorov complexity. Using this technique we provide examples ofeffective and non-sofic shifts on ${\mathbb{Z}}^2$ with very low block complexity: the number of globallyadmissible patterns of size $n\times n$ grows only as a polynomial in $n$. We also show that moreconventional proofs of non-soficness for multi-dimensional effective shifts can be expressed interms of Kolmogorov complexity with unbounded computational resources.

32 pages, 16 figures; v9: minor revision in figures

References in corpus (2)

• Complex Tilings
• Subshifts with sparse traces