Structures without Scattered-Automatic Presentation

@article{Kartzow2013StructuresWS,
  title={Structures without Scattered-Automatic Presentation},
  author={Alexander Kartzow and Philipp Schlicht},
  journal={ArXiv},
  year={2013},
  volume={abs/1304.0912}
}
Bruyere and Carton lifted the notion of finite automata reading infinite words to finite automata reading words with shape an arbitrary linear order \(\mathfrak{L}\). Automata on finite words can be used to represent infinite structures, the so-called word-automatic structures. Analogously, for a linear order \(\mathfrak{L}\) there is the class of \(\mathfrak{L}\)-automatic structures. In this paper we prove the following limitations on the class of \(\mathfrak{L}\)-automatic structures for a… Expand
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References

SHOWING 1-10 OF 25 REFERENCES
Complementation of rational sets on countable scattered linear orderings
Automata-based presentations of infinite structures
Automatic structures
  • Achim Blumensath, E. Grädel
  • Computer Science
  • Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)
  • 2000
Automatic linear orders and trees
Automata on ordinals and automaticity of linear orders
Automatic structures: richness and limitations
Model-theoretic complexity of automatic structures
The Rank of Tree-Automatic Linear Orderings
Automata on linear orderings
...
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3
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