Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Undecidability of Operation Problems for T0L Languages and Subclasses

  • Conference paper
Language and Automata Theory and Applications (LATA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5457))

Abstract

We investigate the decidability of the operation problem for T0L languages and subclasses: Fix an operation on formal languages. Given languages from the family considered (0L languages, T0L languages, or their propagating variants), is the application of this operation to the given languages still a language that belongs to the same language family? Observe, that all the Lindenmayer language families in question are anti-AFLs, that is, they are not closed under homomorphisms, inverse homomorphisms, intersection with regular languages, union, concatenation, and Kleene closure. Besides these classical operations we also consider intersection and substitution, since the language families under consideration are not closed under these operations, too. We show that for all of the above mentioned language operations, except for the Kleene closure, the corresponding operation problems of 0L and T0L languages and their propagating variants are not even semidecidable.

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

Access this chapter

Log in via an institution

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. Bar-Hillel, Y., Perles, M., Shamir, E.: On formal properties of simple phrase structure grammars. Zeitschrift für Phonetik, Sprachwissenschaft und Kommunikationsforschung 14, 143–172 (1961)

    MathSciNet  MATH  Google Scholar 

  2. Bordihn, H., Holzer, M., Kutrib, M.: Unsolvability levels of operation problems for subclasses of context-free languages. Int. J. Found. Comp. Sci. 16, 423–440 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Springer, Heidelberg (1989)

    Book  MATH  Google Scholar 

  4. Dassow, J., Păun, G., Salomaa, A.: On the union of 0L languages. Inform. Process. Letters 47, 59–63 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lindenmayer, A.: Mathematical models for cellular interactions in development I. Filaments with one-sided inputs. J. Theor. Biol. 18, 280–299 (1968)

    Google Scholar 

  6. Lindenmayer, A.: Mathematical models for cellular interactions in development II. Simple and branching filaments with two-sided inputs. J. Theor. Biol. 18, 300–315 (1968)

    Google Scholar 

  7. Maurer, H.A., Salomaa, A., Wood, D.: Pure grammars. Inform. Control 44, 47–72 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  8. Post, E.L.: A variant of a recursively unsolvable problem. Bull. AMS 52, 264–268 (1946)

    Article  MathSciNet  MATH  Google Scholar 

  9. Rozenberg, G., Salomaa, A.: The Mathematical Theory of L Systems. Academic Press, London (1980)

    MATH  Google Scholar 

  10. Salomaa, A.: Formal Languages. Academic Press, London (1973)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Potsdam, August-Bebel-Straße 89, 14482, Potsdam, Germany

    Henning Bordihn

  2. Institut für Informatik, Universität Giessen, Arndtstraße 2, 35392, Giessen, Germany

    Markus Holzer & Martin Kutrib

Authors
  1. Henning Bordihn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Markus Holzer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Martin Kutrib
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Rovira i Virgili University, Av. Catalunya, 35, 43002, Tarragona, Spain

    Adrian Horia Dediu

  2. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Tarragona, Spain

    Armand Mihai Ionescu

  3. European Research Council Executive Agency, 16 Place Rogier, 1210, Brussels, Belgium

    Carlos Martín-Vide

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bordihn, H., Holzer, M., Kutrib, M. (2009). Undecidability of Operation Problems for T0L Languages and Subclasses. In: Dediu, A.H., Ionescu, A.M., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2009. Lecture Notes in Computer Science, vol 5457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00982-2_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00982-2_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00981-5

  • Online ISBN: 978-3-642-00982-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation