Grammars with two-sided contexts

TL;DR

This paper introduces a generalized class of grammars with two-sided context specifications, extending previous models, and provides foundational theory, a normal form, and a polynomial-time parsing algorithm.

Contribution

It extends context grammars to include two-sided contexts, establishing their theoretical framework, normal form, and an O(n^4) parsing algorithm.

Findings

Defined two-sided context grammars and their properties

Developed a normal form for these grammars

Designed a polynomial-time parsing algorithm

Abstract

In a recent paper (M. Barash, A. Okhotin, "Defining contexts in context-free grammars", LATA 2012), the authors introduced an extension of the context-free grammars equipped with an operator for referring to the left context of the substring being defined. This paper proposes a more general model, in which context specifications may be two-sided, that is, both the left and the right contexts can be specified by the corresponding operators. The paper gives the definitions and establishes the basic theory of such grammars, leading to a normal form and a parsing algorithm working in time O(n^4), where n is the length of the input string.