Defining Contexts in Context-Free Grammars

  • Mikhail Barash
  • Alexander Okhotin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7183)


Conjunctive grammars (Okhotin, 2001) are an extension of the standard context-free grammars with a conjunction operation, which maintains most of their practical properties, including many parsing algorithms. This paper introduces a further extension to the model, which is equipped with quantifiers for referring to the left context, in which the substring being defined does occur. For example, a rule \(A \rightarrow a \& \triangleleft{B}\) defines a string a, as long as it is preceded by any string defined by B. The paper gives two equivalent definitions of the model—by logical deduction and by language equations—and establishes its basic properties, including a transformation to a normal form, a cubic-time parsing algorithm, and another recognition algorithm working in linear space.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mikhail Barash
    • 1
    • 2
  • Alexander Okhotin
    • 1
  1. 1.Department of MathematicsUniversity of TurkuTurkuFinland
  2. 2.Turku Centre for Computer ScienceTurkuFinland

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