Sofic Tree-Shifts

We introduce the notion of sofic tree-shifts which corresponds to symbolic dynamical systems of infinite ranked trees accepted by finite tree automata. We show that, contrary to shifts of infinite sequences, there is no unique reduced deterministic irreducible tree automaton accepting an irreducible...

Full description

Saved in:
Bibliographic Details
Published in:Theory of computing systems Vol. 53; no. 4; pp. 621 - 644
Main Authors: Aubrun, Nathalie, Béal, Marie-Pierre
Format: Journal Article
Language:English
Published: Boston Springer US 01.11.2013
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Analysis
Automation
Computer Science
Data Structures and Algorithms
Delay
Design engineering
Dynamical systems
Invariants
Mathematical analysis
Studies
Symbolism
Theory of Computation
Trees
Symbolic dynamics
Tree-shift
Tree automata
ISSN:1432-4350, 1433-0490
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We introduce the notion of sofic tree-shifts which corresponds to symbolic dynamical systems of infinite ranked trees accepted by finite tree automata. We show that, contrary to shifts of infinite sequences, there is no unique reduced deterministic irreducible tree automaton accepting an irreducible sofic tree-shift, but that there is a unique synchronized one, called the Fischer automaton of the tree-shift. We define the notion of almost of finite type tree-shift which are sofic tree-shifts accepted by a tree automaton which is both deterministic and co-deterministic with a finite delay. It is a meaningful intermediate dynamical class in between irreducible finite type tree-shifts and irreducible sofic tree-shifts. We characterize the Fischer automaton of an almost of finite type tree-shift and we design an algorithm to check whether a sofic tree-shift is almost of finite type. We prove that the Fischer automaton is a topological conjugacy invariant of the underlying irreducible sofic tree-shift.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-1
ObjectType-Feature-2
content type line 23
ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-013-9456-1