Multiple Context-Free Grammars and Linear Context-Free Rewriting Systems

Abstract

Multiple Context-Free Grammars (MCFGs) have been introduced by Seki et al. (1991) while the equivalent Linear Context-Free Rewriting Systems (LCFRSs) were independently proposed by Vijay-Shanker, Weir, and Joshi (1987). The central idea is to extend CFGs such that non-terminal symbols can span a tuple of strings that need not be adjacent in the input string. In other words, the yield of a non-terminal symbol can be discontinuous. The grammar contains productions of the form $A_0 \to f[A_1, \dots, A_q]$ where $A_0, \dots, A_q$ are non-terminals and f is a function describing how to compute the yield of $A_{0}$ (a string tuple) from the yields of $A_1, \dots, A_q$.