Abstract
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.
Supported by the Academy of Finland under grant 134860.
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Barash, M., Okhotin, A. (2012). Defining Contexts in Context-Free Grammars. In: Dediu, AH., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2012. Lecture Notes in Computer Science, vol 7183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28332-1_10
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DOI: https://doi.org/10.1007/978-3-642-28332-1_10
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