How to cover a grammar

Abstract

A novel formalism is presented for Earley-like parsers. It accommodates the simulation of non-deterministic pushdown automata. In particular, the theory is applied to non-deterministlc LRoparsers for RTN grammars.

Probabilistic parsing strategies

“…By ignoring the output components of swap transitions we obtain a (P)PDA, which can be mapped to an equivalent (P)CFG as shown above. This observation gives rise to an extension with probabilities of the work on covers by (Nijholt, 1980;Leermakers, 1989).…”

Empirical Risk Minimization for Probabilistic Grammars: Sample Complexity and Hardness of Learning

“…We first show that any context-free grammar with arbitrary degree can be mapped to a corresponding grammar with all N k ≤ 2 that generates derivations equivalent to derivations in the original grammar. Such a grammar is also called a "covering grammar" (Nijholt 1980;Leermakers 1989). Let G be a CFG.…”

Probabilistic parsing strategies

“…By ignoring the output components of swap transitions we obtain a (P)PDA, which can be mapped to an equivalent (P)CFG as shown above. This observation gives rise to an extension with probabilities of the work on covers by [31,23].…”

“…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].…”

“…Two subcomputations are combined through a pop transition by inference rule (23), the intuition of which can be explained as follows. If W occurs as top-of-stack at position i and reading the input up to j results in Y on top of W , and if subsequently reading the input from j to k results in X on top of Y and YX may be replaced by Z by a pop transition, then reading the input from i to k results in Z on top of W .…”