Word automaticity of tree automatic scattered linear orderings is decidable

Authors:
Martin Huschenbett
Affiliations:
Fakultät Informatik und Automatisierung, Fachgebiet Theoretische Informatik, Technische Universität Ilmenau, Postfach, Ilmenau, Germany
Venue:
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Year:
2012

Citing 4
Cited 0

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Abstract

A tree automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. Words can be regarded as specific simple trees and a structure is word automatic if it is encodable using only these trees. The question naturally arises whether a given tree automatic structure is already word automatic. We prove that this problem is decidable for tree automatic scattered linear orderings. Moreover, we show that in case of a positive answer a word automatic presentation is computable from the tree automatic presentation.