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Growing Grammars and Length-reducing Automata

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Abstrakty
EN
Growing context-sensitive grammars were introduced in 1986 as a restricted variant of context-sensitive grammars, where all productions are length increasing. Several interesting properties of these grammars have been shown since then, including polynomial time complexity of the membership problem and machine model characterizations. Various characterizations of the model, efficient recognition algorithm and the properties of its deterministic variant (possessing a characterization by string-rewriting systems) justify the practical value. Moreover, as pointed out by McNaughton in 1999, growing context-sensitive grammars complement the Chomsky hierarchy in a very natural way. This article reviews results on this topic and proposes some open problems.
Wydawca
Rocznik
Strony
193--217
Opis fizyczny
Bibliogr. 40 poz., tab., wykr.
Twórcy
  • Institute of Computer Science, University of Wrocław, Joliot-Curie 15, PL-50-383 Wrocław, Poland, tju@ii.uni.wroc.pl
Bibliografia
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  • [9] S. Cho, D.T. Huynh: Uniform membership for deterministic growing context-sensitive grammars is Pcomplete. Technical Report UTDCS-5-89, Computer Science Department, University of Texas at Dallas, Richardson, Texas 75083, 1989.
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  • [18] T. Jurdziński: The Boolean Closure of Growing Context-Sensitive Languages. Fundam. Inform. 89(2-3), 2008, pp. 289-305.
  • [19] T. Jurdziński, K. Loryś: Lower bound technique for length-reducing automata. Information and Computation, 205(9), 2007, pp. 1387-1412.
  • [20] T. Kasami: An Efficient Recognition and Syntax-Analysis Algorithm for Contex-free Languages. Science Report AFCRL-65-758, Air Force Cambridge Research Laboratory, Bedford,Mass., 1965.
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  • [22] C. Lautemann: One pushdown and a small tape. In: K.W. Wagner (ed.), "Dirk Siefkes zum 50. Geburtstag", Technische Universitaet Berlin and Universitaet Augsburg, 1988.
  • [23] M. Li, P. Vitanyi: An Introduction to Kolmogorov Complexity and its Applications. Springer-Verlag 1993.
  • [24] Liu, L. Y.,Weiner, P.: An infinite hierarchy of intersections of context-free languages. Mathematical Systems Theory, 7, 1973, pp. 185-192.
  • [25] R. McNaughton: An insertion into the Chomsky hierarchy? In: J. Karhumaki, H. A. Maurer, G. Paun, G. Rozenberg (eds.), Jewels are Forever, Contributions on Theoretical Computer Science in Honour of Arto Salomaa, Springer-Verlag, 1999, pp. 204-212.
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  • [27] P. Narendran, K. Krithivasan: On the membership problem for some grammars. COINS Technical Report CAR-TR-267 and CS-TR-1787 and AFOSR-86-0092, Center for Automation Research, University of Maryland, College Park, MD 20742, 1987.
  • [28] G. Niemann: Church-Rosser Languages and Related Classes. PhD Thesis, Universitaet Kassel, 2002.
  • [29] G. Niemann and F. Otto: Restarting automata, Church-Rosser languages, and representations of r.e. languages. In: G. Rozenberg and W. Thomas (eds.), Proc. Developments in Language Theory - Foundations, Applications, and Perspectives, (DLT) 1999,World Scientific, Singapore, 2000, pp. 103-114.
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  • [32] G. Niemann, J.R. Woinowski: The growing context-sensitive languages are the acyclic context-sensitive languages. In: W. Kuich, G. Rozenberg, A. Salomaa (eds.), Proc. Developments in Language Theory (DLT) 2001, LNCS 2295, Springer, 2002, pp. 197-205.
  • [33] C. O'Dunlaing, Natalie Schluter: A shorter proof that palindromes are not a Church-Rosser language, with extensions to almost-confluent and preperfect Thue systems. Theor. Comput. Sci. 411(3), 2010, pp. 677-690.
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  • [36] F. Otto: Restarting Automata and Their Relations to the Chomsky Hierarchy. In: Z. ´Esik, Z. Fülöp (eds.), Proc. Developments in Language Theory (DLT), 2003, LNCS 2710, pp. 55-74.
  • [37] F. Otto, M. Katsura, Y. Kobayashi: Infinite convergent string-rewriting systems and cross-sections for finitely presented monoids. Journal of Symbolic Computation 26(5), 1998, pp. 621-648.
  • [38] J.R. Woinowski. A normal form for Church-Rosser language systems. In A. Middeldorp (ed.), Proc. Rewriting Techniques and Applications (RTA) 2001, LNCS 2051, 2001, Springer, pp. 322-337.
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  • [40] D.H. Younger: Recognition and parsing of context-free languages in time n3. Information and Control, 19, 1967, pp. 189-208.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0022-0056
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