Pattern Complexity of Aperiodic Substitutive Subshifts

05/03/2021
by   Etienne Moutot, et al.
0

This paper aims to better understand the link better understand the links between aperiodicity in subshifts and pattern complexity. Our main contribution deals with substitutive subshifts, an equivalent to substitutive tilings in the context of symbolic dynamics. For a class of substitutive subshifts, we prove a quadratic lower bound on their pattern complexity. Together with an already known upper bound, this shows that this class of substitutive subshifts has a pattern complexity in Θ(n^2). We also prove that the recent bound of Kari and Moutot, showing that any aperiodic subshift has pattern complexity at least mn+1, is optimal for fixed m and n.

READ FULL TEXT
research
02/14/2019

On long words avoiding Zimin patterns

A pattern is encountered in a word if some infix of the word is the imag...
research
03/22/2020

Complexity of randomized algorithms for underdamped Langevin dynamics

We establish an information complexity lower bound of randomized algorit...
research
01/22/2019

Bisimulation Equivalence of First-Order Grammars is ACKERMANN-Complete

Checking whether two pushdown automata with restricted silent actions ar...
research
02/11/2022

Rate-matching the regret lower-bound in the linear quadratic regulator with unknown dynamics

The theory of reinforcement learning currently suffers from a mismatch b...
research
04/28/2020

Tree-depth and the Formula Complexity of Subgraph Isomorphism

For a fixed "pattern" graph G, the colored G-subgraph isomorphism proble...
research
10/25/2021

Parameterized Convexity Testing

In this work, we develop new insights into the fundamental problem of co...
research
04/18/2016

A Repeated Signal Difference for Recognising Patterns

This paper describes a new mechanism that might help with defining patte...

Please sign up or login with your details

Forgot password? Click here to reset