Abstract
We investigate a progression of grammatically defined language families, thecontrol language hierarchy. This hierarchy has been studied recently from the perspective of providing a linguistic framework for natural language syntax. We exhibit a progression of pumping lemmas, one for each family in the hierarchy, thereby showing that the hierarchy is strictly separable.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. V. Aho. Indexed grammars—an extension to context free grammars.J. Assoc. Comput. Mech., 15:647–671, 1968.
S. Ginsburg and E. H. Spanier, Control sets on grammars.Math. Systems Theory, 2:159–177, 1968.
M. A. Harrison.Introduction to Formal Language Theory. Addison-Wesley, Reading, MA, 1978.
G. T. Herman and G. Rozenberg.Developmental Systems and Languages. North-Holland, Amsterdam, 1975.
O. H. Ibarra. Simple matrix languages.Inform, and Control, 17:359–394, 1970.
A. K. Joshi, L. S. Levy, and M. Takahashi. Tree adjunct grammars.J. Comput. System Sci., 10(1), 1975.
T. Kasai. An hierarchy between context-free and context-sensitive languages.J. Comput. System Sci., 4:492–508, 1970.
N. A. Khabbaz. A geometric hierarchy of languages.J. Comput. System Sci., 8:142–157, 1974.
M. A. Palis and S. Shende. Upper bounds on recognition of a hierarchy of non-context-free languages.Theoret. Comput. Sci., 98(2):289–319, May 1992.
D. J. Rozenkrantz. Programmed grammars and classes of formal languages.J. Assoc. Comput. Mech., 16:107–131, 1969.
A. Salomaa. Matrix grammars with a leftmost restriction.Inform, and Control, 20:143–149, 1970.
A. Salomaa.Formal Languages. Academic Press, New York, 1973.
J. W. Thatcher. Tree automata: an informal survey. In A. V. Aho, editor,Currents in the Theory of Computing, pp. 143–172. Prentice-Hall, Englewood Cliffs, NJ, 1973.
K. Vijay-Shanker. A Study of Tree Adjoining Grammars. Ph.D. thesis, University of Pennsylvania, Philadelphia, PA, 1987.
K. Vijay-Shanker and D. J. Weir. The equivalence of four extensions of context-free grammars.Math. Systems Theory, 27:511–546, 1994.
D. J. Weir. Characterizing Mildly Context-Sensitive Grammar Formalisms. Ph.D. Thesis, University of Pennsylvania, Philadelphia, PA, September 1988.
D. J. Weir. A geometric hierarchy beyond context-free languages.Theoret. Comput. Sci., 104:235–261, 1992.
Author information
Authors and Affiliations
Additional information
The research reported in this paper was conducted in part at the Department of Computer and Information Sciences, University of Pennsylvania, Philadelphia, PA 19104, USA, and was supported under ARO Grant DAA29-84-9-0027, NSF Grants MCS-8219116-CER, MCS-82-07294, DCR-84-10413 and MCS-83-05221, and DARPA Grant N00014-85-K-0018.
Rights and permissions
About this article
Cite this article
Palis, M.A., Shende, S.M. Pumping lemmas for the control language hierarchy. Math. Systems Theory 28, 199–213 (1995). https://doi.org/10.1007/BF01303055
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01303055