Lambek grammars with one division are decidable in polynomial time

Authors:
Yury Savateev
Affiliations:
Department of Mathematical Logic, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
Venue:
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Year:
2008

Citing 1
Cited 1

Lambek calculus is NP-complete

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Product-Free Lambek Calculus Is NP-Complete

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Abstract

Lambek grammars provide a useful tool for studying formal and natural languages. The generative power of unidirectional Lambek grammars equals that of context-free grammars. However, no feasible algorithm was known for deciding membership in the corresponding formal languages. In this paper we present a polynomial algorithm for deciding whether a given word belongs to a language generated by a given unidirectional Lambek grammar.