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Unambiguous Separators for Tropical Tree Automata

Authors Thomas Colcombet , Sylvain Lombardy

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LIPIcs.STACS.2020.32.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Algebraic language theory
  • Theory of computation → Quantitative automata
  • Theory of computation → Tree languages
Keywords
  • Tree automata
  • Tropical semiring
  • Separation
  • Unambiguity

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Abstract

In this paper we show that given a max-plus automaton (over trees, and with real weights) computing a function f and a min-plus automaton (similar) computing a function g such that f ⩽ g, there exists effectively an unambiguous tropical automaton computing h such that f ⩽ h ⩽ g.
This generalizes a result of Lombardy and Mairesse of 2006 stating that series which are both max-plus and min-plus rational are unambiguous. This generalization goes in two directions: trees are considered instead of words, and separation is established instead of characterization (separation implies characterization). The techniques in the two proofs are very different.

Cite As Get BibTex

Thomas Colcombet and Sylvain Lombardy. Unambiguous Separators for Tropical Tree Automata. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 32:1-32:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.STACS.2020.32

Author Details

Thomas Colcombet
  • IRIF, CNRS, Université de Paris, Paris, France
Sylvain Lombardy
  • LaBRI, Institut Polytechnique de Bordeaux - Université de Bordeaux - CNRS, France

Funding

  • Colcombet, Thomas: Supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No.670624), and the DeLTA ANR project (ANR-16-CE40-0007).

Acknowledgements

The authors are grateful to the anonymous referees whose remarks and comments have allowed to improve this paper.

References

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