Unidirectional Lambek Grammars in Polynomial Time

@inproceedings{Papakonstantinou2007UnidirectionalLG,
  title={Unidirectional Lambek Grammars in Polynomial Time},
  author={Periklis A. Papakonstantinou and Gerald Penn and Yevgeniy Vahlis},
  year={2007}
}
Lambek Grammars constitute an invaluable proof-theoretic approach to the study of formal and natural languages. We study the long standing open question of the complexity of deciding membership in languages generated by product-free Lambek Grammars. We partially answer this question by showing that the problem for unidirectional product-free Lambek Grammars is decidable in polynomial time and in fact in LOGCFL ⊆ AC. In contrast to earlier work, we do not restrict the lexicon to a single… CONTINUE READING