Entry times in automata with simple defect dynamics
Formal Languages and Automata Theory
2012-08-15 v1 Computational Complexity
Discrete Mathematics
Cellular Automata and Lattice Gases
Abstract
In this paper, we consider a simple cellular automaton with two particles of different speeds that annihilate on contact. Following a previous work by K\r urka et al., we study the asymptotic distribution, starting from a random configuration, of the waiting time before a particle crosses the central column after time n. Drawing a parallel between the behaviour of this automata on a random initial configuration and a certain random walk, we approximate this walk using a Brownian motion, and we obtain explicit results for a wide class of initial measures and other automata with similar dynamics.
Cite
@article{arxiv.1208.2757,
title = {Entry times in automata with simple defect dynamics},
author = {Benjamin Hellouin De Menibus and Mathieu Sablik},
journal= {arXiv preprint arXiv:1208.2757},
year = {2012}
}
Comments
In Proceedings AUTOMATA&JAC 2012, arXiv:1208.2498