μ-Limit Sets of Cellular Automata from a Computational Complexity Perspective - Archive ouverte HAL Access content directly
Journal Articles Journal of Computer and System Sciences Year : 2015

## μ-Limit Sets of Cellular Automata from a Computational Complexity Perspective

(1) , (2) , (3) , (4) , (5)
1
2
3
4
5
Laurent Boyer
Martin Delacourt
Victor Poupet
Mathieu Sablik
Guillaume Theyssier

#### Abstract

This paper concerns $\mu$-limit sets of cellular automata: sets of configurations made of words whose probability to appear does not vanish with time, starting from an initial $\mu$-random configuration. More precisely, we investigate the computational complexity of these sets and of related decision problems. Main results: first, $\mu$-limit sets can have a $\Sigma_3^0$-hard language, second, they can contain only $\alpha$-complex configurations, third, any non-trivial property concerning them is at least $\Pi_3^0$-hard. We prove complexity upper bounds, study restrictions of these questions to particular classes of CA, and different types of (non-)convergence of the measure of a word during the evolution.

#### Domains

Computer Science [cs] Discrete Mathematics [cs.DM]
Loading...

### Dates and versions

hal-00866094 , version 1 (25-09-2013)
hal-00866094 , version 2 (19-06-2015)

### Identifiers

• HAL Id : hal-00866094 , version 2
• ARXIV :
• DOI :

### Cite

Laurent Boyer, Martin Delacourt, Victor Poupet, Mathieu Sablik, Guillaume Theyssier. μ-Limit Sets of Cellular Automata from a Computational Complexity Perspective. Journal of Computer and System Sciences, 2015, 81 (8), pp.1623-1647. ⟨10.1016/j.jcss.2015.05.004⟩. ⟨hal-00866094v2⟩

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

609 View
245 Download

### Share

Gmail Facebook Twitter LinkedIn More