Theory of Computing Systems

, Volume 46, Issue 4, pp 662–672 | Cite as

Unidirectional Lambek Grammars in Polynomial Time



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.


Lambek calculus Unidirectional Lambek grammars Complexity 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Mathematical Logic and Theory of AlgorithmsMoscow State UniversityMoscowRussia

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