Efficient Enumeration Algorithms for Annotated Grammars

TL;DR

This paper introduces annotated grammars, extending context-free grammars with annotations, and presents efficient enumeration algorithms with improved preprocessing times for deriving annotations from input strings.

Contribution

It provides new enumeration algorithms for annotated grammars, reducing preprocessing time from quintic to cubic or quadratic under certain conditions, improving efficiency over prior work.

Findings

Cubic time preprocessing for unambiguous annotated grammars

Quadratic time preprocessing for grammars with a single derivation shape

Linear time preprocessing for generalized regular spanners

Abstract

We introduce annotated grammars, an extension of context-free grammars which allows annotations on terminals. Our model extends the standard notion of regular spanners, and is more expressive than the extraction grammars recently introduced by Peterfreund. We study the enumeration problem for annotated grammars: fixing a grammar, and given a string as input, enumerate all annotations of the string that form a word derivable from the grammar. Our first result is an algorithm for unambiguous annotated grammars, which preprocesses the input string in cubic time and enumerates all annotations with output-linear delay. This improves over Peterfreund's result, which needs quintic time preprocessing to achieve this delay bound. We then study how we can reduce the preprocessing time while keeping the same delay bound, by making additional assumptions on the grammar. Specifically, we present a class of grammars which only have one derivation shape for all outputs, for which we can enumerate with quadratic time preprocessing. We also give classes that generalize regular spanners for which linear time preprocessing suffices.