Tree-automatic scattered linear orders

  title={Tree-automatic scattered linear orders},
  author={Sanjay Jain and Bakhadyr Khoussainov and Philipp Schlicht and Frank Stephan},
  journal={Theor. Comput. Sci.},
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
4 Citations
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This thesis studies the model-theoretic complexity of automatic linear orders in terms of two complexity measures: the finite-condensation rank and the Ramsey degree. Expand
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Isomorphisms of scattered automatic linear orders
  • D. Kuske
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 2014
Abstract We prove that the isomorphism of scattered tree-automatic linear orders as well as the existence of automorphisms of scattered word-automatic linear orders are undecidable. For the existenceExpand
L O ] 2 5 A pr 2 01 2 Isomorphisms of scattered automatic linear orders
We prove that the isomorphism of scattered tree automatic linear orders as well as the existence of automorphisms of scattered word automatic linear orders are undecidable. For the existence ofExpand


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Automatic linear orders and trees
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Word Automaticity of Tree Automatic Scattered Linear Orderings Is Decidable
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Automatic structures
  • Achim Blumensath, E. Grädel
  • Computer Science
  • Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)
  • 2000
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Automatic structures are finitely presented structures where the universe and all relations can be recognized by finite automata. It is known that the isomorphism problem for automatic structures isExpand
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