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.
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Huschenbett, M. (2012). Word Automaticity of Tree Automatic Scattered Linear Orderings Is Decidable. In: Cooper, S.B., Dawar, A., Löwe, B. (eds) How the World Computes. CiE 2012. Lecture Notes in Computer Science, vol 7318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30870-3_32
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DOI: https://doi.org/10.1007/978-3-642-30870-3_32
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