Reformulating Global Grammar Constraints

TL;DR

This paper presents a method to convert context-free grammars into automata for global constraints, and demonstrates that automaton minimization after unfolding can lead to more efficient problem solving in rostering applications.

Contribution

It introduces an algorithm for transforming context-free grammars into automata and shows that post-unfolding minimization improves automaton compactness and computational efficiency.

Findings

Minimizing automata after unfolding yields smaller automata.

Transformations improve the size and solvability of rostering problems.

Automaton minimization techniques enhance constraint propagation speed.

Abstract

An attractive mechanism to specify global constraints in rostering and other domains is via formal languages. For instance, the Regular and Grammar constraints specify constraints in terms of the languages accepted by an automaton and a context-free grammar respectively. Taking advantage of the fixed length of the constraint, we give an algorithm to transform a context-free grammar into an automaton. We then study the use of minimization techniques to reduce the size of such automata and speed up propagation. We show that minimizing such automata after they have been unfolded and domains initially reduced can give automata that are more compact than minimizing before unfolding and reducing. Experimental results show that such transformations can improve the size of rostering problems that we can 'model and run'.