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Unidirectional Lambek Grammars in Polynomial Time

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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.

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References

  1. Aarts, E., Trautwein, K.: Non-associative Lambek categorial grammar in polynomial time. Math. Log. Q. 41, 476–484 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Buszkowski, W.: The equivalence of unidirectional Lambek categorial grammars and context-free grammars. Z. Math. Log. Grundl. Math. 31(4), 369–384 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  3. de Groote, P.: The non-associative Lambek calculus with product in polynomial time. In: Murray, N.V. (ed.) Automated Reasoning with Analytic Tableaux and Related Methods, pp. 128–139. Springer, Berlin (1999)

    Chapter  Google Scholar 

  4. Lambek, J.: The mathematics of sentence structure. Am. Math. Mon. 65(3), 154–170 (1958)

    Article  MATH  MathSciNet  Google Scholar 

  5. Lambek, J.: On the calculus of syntactic types. In: Jakobson, R. (ed.) Structure of Language and Its Mathematical Aspects. Proc. Symposia Appl. Math., vol. 12, pp. 166–178. Amer. Math. Soc., Providence (1961)

    Google Scholar 

  6. Pentus, M.: Lambek calculus is NP-complete. Theor. Comput. Sci. 357(1–3), 186–201 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Pentus, M.: Lambek grammars are context free. In: Proceedings of the 8th Annual IEEE Symposium on Logic in Computer Science, pp. 429–433 (1993)

  8. Savateev, Y.: The derivability problem for Lambek calculus with one division. Technical report, Utrecht University, Artificial Intelligence Preprint Series, no. 56 (2006)

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Authors and Affiliations

  1. Department of Mathematical Logic and Theory of Algorithms, Moscow State University, Moscow, Russia

    Yury Savateev

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  1. Yury Savateev
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Correspondence to Yury Savateev.

Additional information

This research was supported in part by the Russian Foundation for Basic Research grant 08-01-00399, and by the Dutch-Russian cooperation program NWO/RFBR, project No. 047.017.014.

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Savateev, Y. Unidirectional Lambek Grammars in Polynomial Time. Theory Comput Syst 46, 662–672 (2010). https://doi.org/10.1007/s00224-009-9208-4

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  • DOI: https://doi.org/10.1007/s00224-009-9208-4

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