Word Automaticity of Tree Automatic Scattered Linear Orderings Is Decidable
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2012
- DOI:
- 10.48550/arXiv.1201.5070
- arXiv:
- arXiv:1201.5070
- Bibcode:
- 2012arXiv1201.5070H
- Keywords:
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- Computer Science - Logic in Computer Science;
- F.4.1
- E-Print:
- 19 pages, 2 figures