An extension of context-free grammars with one-sided context specifications

Abstract

The paper introduces an extension of context-free grammars equipped with an operator for referring to the left context of the substring being defined. For example, a rule A→a&◁B defines a symbol a, as long as it is preceded by a string defined by B. The conjunction operator in this example is taken from conjunctive grammars (Okhotin, 2001), which are an extension of ordinary context-free grammars that maintains most of their practical properties, including many parsing algorithms. This paper gives two equivalent definitions of grammars with left contexts—by logical deduction and by language equations—and establishes their basic properties, including a transformation to a normal form and a cubic-time parsing algorithm, with a square-time version for unambiguous grammars.