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Non-erasing Variants of the Chomsky–Schützenberger Theorem

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

Abstract

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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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

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