Commutation-Augmented Pregroup Grammars and Mildly Context-Sensitive Languages
First Online: 27 November 2007 DOI:
Cite this article as: Francez, N. & Kaminski, M. Stud Logica (2007) 87: 295. doi:10.1007/s11225-007-9088-z Abstract
The paper presents a generalization of pregroup, by which a freely-generated pregroup is augmented with a finite set of
commuting inequations, allowing limited commutativity and cancelability. It is shown that grammars based on the commutation-augmented pregroups generate mildly context-sensitive languages. A version of Lambek’s switching lemma is established for these pregroups. Polynomial parsability and semilinearity are shown for languages generated by these grammars. Keywords Formal language theory pregroup grammars mildly context-sensitive languages
Special Issue Categorial Grammars and Pregroups Edited by
Wojciech Buszkowski and Anne Preller References
Buszkowski W., ‘Lambek grammars based on pregroups’, in P. De Groote, G. Morill, and Ch. Retoré (eds.),
Logical Aspects of Computational Linguistics, vol. 2099 of Lecture Notes in Computer Science, Springer Verlag, Berlin Heidelberg, 2001, pp. 95–109.
Francez, N., and M. Kaminski,
Pushdown automata with cancellation and commutation-augmented pregroup grammars, in R. Loos, S.Z. Fazekas, and C. Martín-Vide (eds.), Pre-proceedings of the 1st International Conference on Language and Automata Theory and Applications (LATA07), Tarragona, Spain, March 29 – April 4, 2007, pp. 7–25.
Hopcroft J.E., Ulmann J.D. (1979) Introduction to Automata Theory, Languages and Computation. Addison Wesley, New York
Lambek, J., ‘Type grammars revisited’, in A. Lecomte, F. Lamarche, and G. Perrier (eds.),
Logical Aspects of Computational Linguistics, vol. 1582 of Lecture Notes in Computer Science, Springer Verlag, Berlin Heidelberg, 1999, pp. 1–27.
Lewis H.R, Papadimitriou Ch.H. (1981). Elements of the Theory of Computation. Prentice Hall, Englewood Cliffs, NJ
Michaelis, J., and M. Kracht, ‘Semilinearity as a syntactic invariant’, in Ch. Retoré (ed.),
Logical Aspects of Computational Linguistics, vol. 1328 of Lecture Notes in Computer Science, Springer Verlag, Berlin Heidelberg, 1997, pp. 329–345.
Parikh, R. J., ‘On context-free languages’,
Journal of the ACM 13, 4 (1966), 570–581
Vijay-Shanker K., David J. Weir (1994). The equivalence of four extensions of context-free grammars’. Mathematical System Theory 27: 511–546
CrossRef Google Scholar Copyright information
© Springer Science+Business Media B.V. 2007