Complex tilings

Authors:
Bruno Durand;Leonid Levin;Alexander Shen
Affiliations:
Laboratoire d'Informatique de, Marseille - CMI, 39, rue Joliot-Curie, 13453 Marseille, France;Boston University, Computer Science department, 111 Cummington St., Boston, MA;Institute of Problems of Information Transmission, Moscow, Russia
Venue:
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Year:
2001

Citing 4
Cited 10

Average case complete problems

SIAM Journal on Computing
Average case completeness

Journal of Computer and System Sciences
An introduction to Kolmogorov complexity and its applications (2nd ed.)

An introduction to Kolmogorov complexity and its applications (2nd ed.)
Tilings and quasiperiodicity

Theoretical Computer Science

De la logique aux pavages

Theoretical Computer Science
An Almost Totally Universal Tile Set

TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
High Complexity Tilings with Sparse Errors

ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Constructing New Aperiodic Self-simulating Tile Sets

CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Universal tilings

STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A topological study of tilings

TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Tilings: Simulation and universality

Mathematical Structures in Computer Science
Forbidden substrings, kolmogorov complexity and almost periodic sequences

STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Tilings robust to errors

LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Simulation of Effective Subshifts by Two-dimensional Subshifts of Finite Type

Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the minimal complexity of tilings of a plane with a given tile set. We note that any tile set admits either no tiling or some tiling with \ooo(n) Kolmogorov complexity of its (n\times n)-squares. We construct tile sets for which this bound is nearly tight: all tilings have complexity n/r(n), given any unbounded computable monotone r. This adds a quantitative angle to classical results on non-recursivity of tilings -- that we also develop in terms of Turing degrees of unsolvability.