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Generalized Derivations with Synchronized Context-Free Grammars

  • Markus Holzer
  • Sebastian Jakobi
  • Ian McQuillan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7410)

Abstract

Synchronized context-free grammars are special context-free grammars together with a relation which must be satisfied between every pair of paths from root to leaf in a derivation tree, in order to contribute towards the generated language. In the past, only the equality relation and the prefix relation have been studied, with both methods generating exactly the ET0L languages. In this paper, we study arbitrary relations, and in particular, those defined by a transducer. We show that if we use arbitrary a-transducers, we can generate all recursively enumerable languages, and moreover, there exists a single fixed transducer, even over a two letter alphabet, which allows to generate all recursively enumerable languages. We also study the problem over unary transducers. Although it is left open whether or not we can generate all recursively enumerable languages with unary transducers, we are able to demonstrate that we can generate all ET0L languages as well as a language that is not an indexed language. Only by varying the transducer used to define the relation, this generalization is natural, and can give each of the following language families: context-free languages, a family between the E0L and ET0L languages, ET0L languages, and recursively enumerable languages.

Keywords

Turing Machine Generalize Derivation Regular Language Derivation Tree Language Family 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Aho, A.V.: Indexed grammars—an extension of context-free grammars. J. ACM 15(4), 647–671 (1968)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bordihn, H., Holzer, M.: On the computational complexity of synchronized context-free languages. J. Univ. Comput. Sci. 8(2), 119–140 (2002)MathSciNetGoogle Scholar
  3. 3.
    Gilman, R.H.: A shrinking lemma for indexed languages. Theoret. Comput. Sci. 163(1-2), 277–281 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley (1979)Google Scholar
  5. 5.
    Hromkovič, J., Karhumäki, J., Rovan, B., Slobodová, A.: On the power of synchronization in parallel computations. Discrete Appl. Math. 32, 155–182 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Hromkovič, J., Rovan, B., Slobodová, A.: Deterministic versus nondeterministic space in terms of synchronized alternating machines. Theoret. Comput. Sci. 132, 319–336 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Jürgensen, H., Salomaa, K.: Block-synchronized context-free grammars. In: Du, D.Z., Ko, J.I. (eds.) Advances in Algorithms, Languages, and Complexity, pp. 111–137. Kluwer (1997)Google Scholar
  8. 8.
    McQuillan, I.: Descriptional complexity of block-synchronization context-free grammars. J. Autom. Lang. Comb. 9(2/3), 317–332 (2004)MathSciNetzbMATHGoogle Scholar
  9. 9.
    McQuillan, I.: The generative capacity of block-synchronized context-free grammars. Theoret. Comput. Sci. 337(1-3), 119–133 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Rozenberg, G., Salomaa, A.: The Mathematical Theory of L Systems, Pure and Applied Mathematics, vol. 90. Academic Press (1980)Google Scholar
  11. 11.
    Salomaa, A.: Formal Languages. ACM Monograph Series. Academic Press (1973)Google Scholar
  12. 12.
    Salomaa, K.: Synchronized tree automata. Theoret. Comput. Sci. 127, 25–51 (1994)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Markus Holzer
    • 1
  • Sebastian Jakobi
    • 1
  • Ian McQuillan
    • 2
  1. 1.Institut für InformatikUniversität GiessenGiessenGermany
  2. 2.Department of Computer ScienceUniversity of SaskatchewanSaskatoonCanada

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