An optimal tabular parsing algorithm

Abstract

In this paper we relate a number of parsing algorithms which have been developed in very di erent areas of parsing theory, and which include deterministic algorithms, tabular algorithms, and a parallel algorithm. We show that these algorithms are based on the same underlying ideas.By relating existing ideas, we hope to provide an opportunity to improve some algorithms based on features of others. A second purpose of this paper is to answer a question which has come up in the area of tabular parsing, namely how to obtain a parsing algorithm with the property that the table will contain as little entries as possible, but without the possibility that two entries represent the same subderivation.

Probabilistic parsing strategies

“…It was originally formulated as a parsing strategy for extended CFGs [32,23], but its re-striction to normal CFGs is interesting in its own right, as argued by [27]. ELR parsing for CFGs is also related to the tabular algorithm from [48].…”

“…In other words, for a given item, we investigate all possible ways of deriving that item as the consequent of different inference rules with different antecedents. For example, the second line in the right-hand side of equation (27), can be seen as the backward application of inference rule (21).…”

“…p tab (forward (X, Y, i, j)) = (27) δ(X = ⊥ ∧ Y = X init ∧ i = j = 0) + Figure 6: Recursive functions to determine probabilities of table items.…”

Survey of the State of the Art in Human Language Technology

“…In practice, most algorithms for CFGs run much better than the worst case and the real limiting factor in practice is the size of the grammar. For a general discussion of parsing strategies, see Leermakers (1993);Nedderhoff (1994);Sikkel (1994).…”

Bidirectional Push Down Automata

“…This approach has been successfully applied to the design of parsing algorithms for context-free grammars that read the input string left-to-right [5,6]. In this article, we define new models of push-down automata which can start reading the input string in any position, spanning to the left and to the right to include substrings which were themselves read in the same bidirectional way.…”