Restricted Global Grammar Constraints

TL;DR

This paper explores the computational complexity of the GRAMMAR constraint over restricted classes of context-free grammars, providing new algorithms and applications for linear grammars in constraint programming.

Contribution

It demonstrates that detecting disentailment remains hard for certain restricted grammars and introduces a quadratic-time propagator for linear grammars, applying it to encode the EDITDISTANCE constraint.

Findings

Disentailment detection is as hard for deterministic and unambiguous grammars as for unrestricted grammars.

A quadratic-time propagator for linear grammars is developed.

Weighted linear GRAMMAR constraints can efficiently encode the EDITDISTANCE constraint.

Abstract

We investigate the global GRAMMAR constraint over restricted classes of context free grammars like deterministic and unambiguous context-free grammars. We show that detecting disentailment for the GRAMMAR constraint in these cases is as hard as parsing an unrestricted context free grammar.We also consider the class of linear grammars and give a propagator that runs in quadratic time. Finally, to demonstrate the use of linear grammars, we show that a weighted linear GRAMMAR constraint can efficiently encode the EDITDISTANCE constraint, and a conjunction of the EDITDISTANCE constraint and the REGULAR constraint