Computing first and follow functions for feature theoretic grammars

Abstract

This paper describes an algorithm for the computation of FIRST and FOLLOW sets for use with feature-theoretic grammars, in which the value of the sets consists of pairs of featuretheoretic categories. The algorithm preserves as much information from the grammars as possible, using negative restriction to de ne equivalence classes. Addition of a simple data structure leads to an order of magnitude improvement in execution time over a naive implementation.

Generalized LR parsing for extensions of context-free grammars

“…Thus the construction of the parsing tables may be a non terminating process. A solution to this problem is to use positive restrictors (Shieber 1985) or negative restrictors (Trujillo 1994) to de ne a nite number of equivalence classes into which the in nite number of nonterminals may be sorted. The restrictor must be applied to obtain the compiled information: the rst and follow functions, the closure of the LR automaton and the action and goto tables.…”

Connectivity in bag generation

“…Outer domains are defined as follow: Definition 3 {(Sign, Lcx, Binds) I Sign C N tO T, Lcx ~ T and there exists a derivation Oe ~ /31Signt /32 LeJ /33 or a ~ f11Lez] /32,S'iqnl /33, and Sign' a unifier for Sign, Lez j a unifier for Lcx, and Binds the set of all path pairs <SignPath, LexPalh> such thai Sign':SignPath is Ioken identical with LezS :LexPath} Intuitively, the outer domains indicate that preterminal category Lex ('an appear in a complete sentence with subconstituent Sign, such that l,cx is not a leaf of Sign. Using ideas from data flow analysis (Kennedy, 1981), predictive parser constructions (Aho et al, 1986) and feature grammar compilation (Trujillo, 1994) it is possible to construct such a set of triples. Outer domains thus represent elements whi(:h may lie outside a subtree of category Sign in a complete sentential they would be indicated through paths such as SYNSEM :LOCAL:CONTI,INT:INI) EX.…”

“…First, the inner domains of the grammar are calculated. This involves the calculation of the fixed point of set equations, analogous to those used in the construction of First sets for predictive parsers (Aho et al, 1986;Trujillo, 1994). Given the inner domains of each category in the grammar, the construction of the outer domains involves the computation of the lixed point of set equations relating the outer domain of a category to the inner domain of its sisters and to the outer domain of its mother, in a manner analogous to the eoinputation of Follow sets.…”