Abstract
In this paper we propose a generalization of the local internal contextual grammars, introduced by Ilie in 1997, namely the k-local internal contextual grammars. These grammars are, in fact, classical internal contextual grammars, but their only permitted derivations are those that can be described in a restricted manner (that depends on the number k). Using this formalism we define different classes of languages, and obtain a series of language theoretic results for them. Also, we show that the membership problem for k-local internal contextual grammars with polynomial choice can be solved in polynomial time. This seems interesting to us, as it shows that the descriptional restrictions on the derivations of a grammar reflect on the computational efficiency of accepting the language generated by that grammar.
The work of Florin Manea is supported by the Alexander von Humboldt Foundation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Marcus, S.: Contextual grammars. Revue Roum. Math. Pures Appl. 14, 1525–1534 (1969)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Berlin (1997)
Păun, G.: Marcus Contextual Grammars. Kluwer Publ. House, Dordrecht (1998)
Gramatovici, R., Martín-Vide, C.: Sorted dependency insertion grammars. Theor. Comput. Sci. 354(1), 142–152 (2006)
Gramatovici, R.: An efficient parser for a class of contextual languages. Fundam. Inform. 33, 211–238 (1998)
Enguix, G.B., Gramatovici, R.: Parsing with active p automata. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 31–42. Springer, Heidelberg (2004)
Gramatovici, R., Manea, F.: Parsing local internal contextual languages with context-free choice. Fundam. Inform. 64, 171–183 (2005)
Gramatovici, R., Manea, F.: A cyk-based parser for local internal contextual grammars with context-free choice. In: Proc. AFL 2005, pp. 31–42 (2005)
Harbusch, K.: An efficient online parser for contextual grammars with at most context-free selectors. In: Gelbukh, A. (ed.) CICLing 2003. LNCS, vol. 2588, pp. 168–179. Springer, Heidelberg (2003)
Harbusch, K.: Parsing contextual grammars with linear, regular and context-free selectors. In: Grammars and Automata for String Processing. Topics in Computer Mathematics, vol. 9, pp. 45–54. Taylor and Francis, Abington (2003)
Jancar, P., Mráz, F., Plátek, M., Procházka, M., Vogel, J.: Restarting automata, marcus grammars and context-free languages. Developments in Language Theory, 102–111 (1995)
Mráz, F., Plátek, M., Procházka, M.: Restarting automata, deleting and marcus grammars. In: Recent Topics in Mathematical and Computational Linguistics, pp. 218–233. Romanian Academy Publishing House (2000)
Ilie, L.: On computational complexity of contextual languages. Theor. Comput. Sci. 183(1), 33–44 (1997)
Gramatovici, R., Manea, F.: k-Local Internal Contextual Grammars. Technical report, Otto-von-Guericke-Universität Magdeburg, Fakultät für Informatik (2011), http://theo.cs.uni-magdeburg.de/pubs/preprints/pp-afl-2011-06.pdf
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gramatovici, R., Manea, F. (2011). k-Local Internal Contextual Grammars. In: Holzer, M., Kutrib, M., Pighizzini, G. (eds) Descriptional Complexity of Formal Systems. DCFS 2011. Lecture Notes in Computer Science, vol 6808. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22600-7_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-22600-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22599-4
Online ISBN: 978-3-642-22600-7
eBook Packages: Computer ScienceComputer Science (R0)