Undecidability of Operation Problems for T0L Languages and Subclasses

  • Henning Bordihn
  • Markus Holzer
  • Martin Kutrib
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5457)


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.


Regular Language Language Family Sentential Form Operation Problem Formal Language Theory 
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  1. 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)MathSciNetzbMATHGoogle Scholar
  2. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Springer, Heidelberg (1989)CrossRefzbMATHGoogle Scholar
  4. 4.
    Dassow, J., Păun, G., Salomaa, A.: On the union of 0L languages. Inform. Process. Letters 47, 59–63 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 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. 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. 7.
    Maurer, H.A., Salomaa, A., Wood, D.: Pure grammars. Inform. Control 44, 47–72 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Post, E.L.: A variant of a recursively unsolvable problem. Bull. AMS 52, 264–268 (1946)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Rozenberg, G., Salomaa, A.: The Mathematical Theory of L Systems. Academic Press, London (1980)zbMATHGoogle Scholar
  10. 10.
    Salomaa, A.: Formal Languages. Academic Press, London (1973)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Henning Bordihn
    • 1
  • Markus Holzer
    • 2
  • Martin Kutrib
    • 2
  1. 1.Institut für InformatikUniversität PotsdamPotsdamGermany
  2. 2.Institut für InformatikUniversität GiessenGiessenGermany

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