Non-erasing Variants of the Chomsky–Schützenberger Theorem

  • Alexander Okhotin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7410)


The famous theorem by Chomsky and Schützenberger (“The algebraic theory of context-free languages”, 1963) states that every context-free language is representable as h(D k  ∩ R), where D k is the Dyck language over \(k \geqslant 1\) pairs of brackets, R is a regular language and h is a homomorphism. This paper demonstrates that one can use a non-erasing homomorphism in this characterization, as long as the language contains no one-symbol strings. If the Dyck language is augmented with neutral symbols, the characterization holds for every context-free language using a letter-to-letter homomorphism.


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  1. 1.
    Chomsky, N., Schützenberger, M.P.: The algebraic theory of context-free languages. In: Braffort, Hirschberg (eds.) Computer Programming and Formal Systems, pp. 118–161. North-Holland, Amsterdam (1963)CrossRefGoogle Scholar
  2. 2.
    Engelfriet, J.: An elementary proof of double Greibach normal form. Information Processing Letters 44(6), 291–293 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Ginsburg, S.: The Mathematical Theory of Context-Free Languages. McGraw-Hill (1966)Google Scholar
  4. 4.
    Harrison, M.: Introduction to Formal Language Theory. Addison-Wesley (1978)Google Scholar
  5. 5.
    Lallement, G.J.: Semigroups and Combinatorial Applications. John Wiley and Sons (1979)Google Scholar
  6. 6.
    Rozenkrantz, D.J.: Matrix equations and normal forms for context-free grammars. Journal of the ACM 14(3), 501–507 (1967)CrossRefGoogle Scholar
  7. 7.
    Salomaa, A.: Formal Languages. Academic Press (1973)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alexander Okhotin
    • 1
  1. 1.Department of MathematicsUniversity of TurkuTurkuFinland

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