Choosing Word Occurrences for the Smallest Grammar Problem

The smallest grammar problem - namely, finding a smallest context-free grammar that generates exactly one sequence - is of practical and theoretical importance in fields such as Kolmogorov complexity, data compression and pattern discovery. We propose to focus on the choice of the occurrences to be rewritten by non-terminals. We extend classical offline algorithms by introducing a global optimization of this choice at each step of the algorithm. This approach allows us to define the search space of a smallest grammar by separating the choice of the non-terminals and the choice of their occurrences. We propose a second algorithm that performs a broader exploration by allowing the removal of useless words that were chosen previously. Experiments on a classical benchmark show that our algorithms consistently find smaller grammars then state-ofthe-art algorithms.

• Type: Conference
• Year: 2010
• Where: LATA
• Authors: Rafael Carrascosa, François Coste, Matthias Gallé, Gabriel G. Infante Lopez
• Keywords: Automata Theory, LATA 2010, Smallest Context-free Grammar, Smallest Grammar, Smallest Grammar Problem