𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Group structured linear cellular automata over Zm

✍ Scribed by Tadakazu Sato

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
285 KB
Volume
49
Category
Article
ISSN
0022-0000

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we introduce group structured linear cellular automata which appear naturally in the process of finding their inverse automata and show that the set of local maps of such automata forms a group with the star operation and the problem of finding its inverse linear cellular automaton can be reduced to that of finding its inverse element of the group. Furthermore, it is shown that such groups regardless of their scopes are isomorphic to each other.

πŸ“œ SIMILAR VOLUMES

Linear cellular automata over Zm
Linear cellular automata over Zm
✍ Masanobu ItΓ΄; Nobuyasu Γ”sato; Masakazu Nasu πŸ“‚ Article πŸ“… 1983 πŸ› Elsevier Science 🌐 English βš– 969 KB
Ergodic characterization of linear cellu
Ergodic characterization of linear cellular automata over Zm
✍ Tadakazu Sato πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 561 KB

In this paper, we introduce a set E(f,) which consists of all points rEZ2 such that the composite map o'(&) of a shift transformation or and a parallel map fm is non-ergodic. We then show that the properties of parallel maps foe such as finite orderedness, infinite orderedness, injectivity, surjecti

Ergodicity, transitivity, and regularity
Ergodicity, transitivity, and regularity for linear cellular automata over Zm
✍ Gianpiero Cattaneo; Enrico Formenti; Giovanni Manzini; Luciano Margara πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 142 KB

We study the dynamical behavior of D-dimensional linear cellular automata over Zm. We provide an easy-to-check necessary and su cient condition for a D-dimensional linear cellular automata over Z m to be ergodic and topologically transitive. As a byproduct, we get that for linear cellular automata e

A complete and efficiently computable to
A complete and efficiently computable topological classification of D-dimensional linear cellular automata over Zm
✍ Giovanni Manzini; Luciano Margara πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 962 KB

We study the dynamical behavior of D-dimensional linear cellular automata over Zm. We provide easy-to-check necessary and sufficient conditions for a D-dimensional linear cellular automata over Zm to be sensitive to initial conditions, positively expansive, strongly transitive, and equicontinuous. A