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.
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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
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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
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