Skip to main content

On the Complexity of the Syntax of Tree Languages

Dedicated to Prof. Werner Kuich on the occasion of his retirement

  • Conference paper
Algebraic Informatics (CAI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5725))

Included in the following conference series:

Abstract

The syntactic complexity of a tree language is defined according to the number of the distinct syntactic classes of all trees with a fixed yield length. This leads to a syntactic classification of tree languages and it turns out that the class of recognizable tree languages is properly contained in that of languages with bounded complexity. A refined syntactic complexity notion is also presented, appropriate exclusively for the class of recognizable tree languages. A tree language is recognizable if and only if it has finitely many refined syntactic classes. The constructive complexity of a tree automaton is also investigated and we prove that for any reachable tree automaton it is equal with the refined syntactic complexity of its behavior.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Bozapalidis, S.: Picture languages: Recognizability, Syntax and Context Freeness (submitted)

    Google Scholar 

  2. Bozapalidis, S., Kalampakas, A.: Recognizability of graph and pattern languages. Acta Informatica 42, 553–581 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Engelfriet, J.: Tree Automata and Tree Grammars, DAIMNI FN-10, University of Aarhus (1975)

    Google Scholar 

  4. Gécseg, F., Steinby, M.: Tree Automata. Akademiai Kiado, Budapest (1984)

    Google Scholar 

  5. Gécseg, F., Steinby, M.: Tree Languages. Handbook of Formal Languages 3, 1–68 (1997)

    MathSciNet  Google Scholar 

  6. Kalampakas, A.: The syntactic complexity of eulerian graphs. In: Bozapalidis, S., Rahonis, G. (eds.) CAI 2007. LNCS, vol. 4728, pp. 208–217. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bozapalidis, S., Kalampakas, A. (2009). On the Complexity of the Syntax of Tree Languages. In: Bozapalidis, S., Rahonis, G. (eds) Algebraic Informatics. CAI 2009. Lecture Notes in Computer Science, vol 5725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03564-7_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03564-7_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03563-0

  • Online ISBN: 978-3-642-03564-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics