# Tree-automatic scattered linear orders

@article{Jain2016TreeautomaticSL, title={Tree-automatic scattered linear orders}, author={Sanjay Jain and Bakhadyr Khoussainov and Philipp Schlicht and Frank Stephan}, journal={Theor. Comput. Sci.}, year={2016}, volume={626}, pages={83-96} }

Tree-automatic linear orders on regular tree languages are studied. It is shown that there is no tree-automatic scattered linear order, and therefore no tree-automatic well-order, on the set of all finite labeled trees, and that a regular tree language admits a tree-automatic scattered linear order if and only if for some n, no binary tree of height n can be embedded into the union of the domains of its trees. Hence the problem whether a given regular tree language can be ordered by a scattered… Expand

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