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
4 Citations
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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

References

SHOWING 1-10 OF 44 REFERENCES
The Rank of Tree-Automatic Linear Orderings
TLDR
It is proved that the FC-rank of every tree-automatic linear ordering is below omega^omega, and an analogue for tree- automatic linear orderings where the branching complexity of the trees involved is bounded is shown. Expand
Automatic linear orders and trees
TLDR
It is shown that every infinite path in an automatic tree with countably many infinite paths is a regular language. Expand
Word Automaticity of Tree Automatic Scattered Linear Orderings Is Decidable
TLDR
It is proved that the problem of whether a given tree automatic structure is already word automatic is decidable for tree automatic scattered linear orderings and in case of a positive answer a word automatic presentation is computable from the tree automatic presentation. Expand
Automatic structures
  • Achim Blumensath, E. Grädel
  • Computer Science
  • Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)
  • 2000
TLDR
This work determines the complexity of model checking and query evaluation on automatic structures for fragments of first-order logic and gives model-theoretic characterisations for automatic structures via interpretations. Expand
MSO on the Infinite Binary Tree: Choice and Order
TLDR
It is shown that every infinite binary tree with a well-founded order has an undecidable MSO-theory, and some applications of the result concerning unambiguous tree automata and definability of winning strategies in infinite games are discussed. Expand
Model-theoretic complexity of automatic structures
TLDR
The following results are proved: The ordinal height of any automatic well-founded partial order is bounded by ωω, and the ordinal heights of automaticWell-founded relations are unbounded below (ω1CK). Expand
A hierarchy of tree-automatic structures
TLDR
It is obtained that there exist infinitely many ωn- automatic, hence also ω-tree-automatic, atomless boolean algebras, which are pairwise isomorphic under the continuum hypothesis CH and pairwise non isomorph under an alternate axiom AT, strengthening a result of [14]. Expand
The isomorphism problem on classes of automatic structures with transitive relations
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
Decidability of second-order theories and automata on infinite trees
Introduction. In this paper we solve the decision problem of a certain secondorder mathematical theory and apply it to obtain a large number of decidability results. The method of solution involvesExpand
Pumping for ordinal-automatic structures
TLDR
A pumping lemma for alpha-automata (processing finite alpha-words, i.e., words of length alpha that have one fixed letter at all but finitely many positions) is developed and a sharp bound on the height of the finite word alpha-automatic well-founded order forests is provided. Expand
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