Summary
This review paper will report on some recent discoveries in the area of Formal Languages, chiefly by F. Otto, G. Buntrock and G. Niemann. These discoveries have pointed out certain break-throughs connected with the concept of growing context-sensitive languages, which originated in the 1980’s with a paper by E. Dahlhaus and M.K. Warmuth. One important result is that the deterministic growing context-sensitive languages turn out to be identical to an interesting family of formal languages definable in a certain way by confluent reduction systems.
Paljon onnea, Arto. In other words, Onnellista syntymäpäiää.
This is a preview of subscription content, log in via an institution to check access.
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
Gladkij, A.W., “On the complexity of derivations in context-sensitive grammars”, Algebri i Logika Sem., vol. 3, pp. 29–44, 1964. In Russian.
Book, R.V. Grammars with time functions, Dissertation, Harvard University, 1969.
Salomaa, A., Theory of Automata, Pergamon Press, Oxford, England, 1969.
Book, R.V., “Confluent and other types of Thue systems”, J. ACM, vol. 29, pp. 171–182, 1982.
Dahlhaus, E. and M.K. Warmuth, “Membership for growing context-sensitive grammars is polynomial”, J. Computer and System Sciences, vol. 33, pp. 456–472, 1986.
Lautemann, C. “One pushdown and a small tape”, in Dirk Siefkes zum 50. Geburtstag (K.W. Wagner, ed.), pp. 42–47, Technische Universität Berlin and Universität Augsburg, 1988.
McNaughton, R., P. Narendran and F. Otto, “Church-Rosser Thue systems and formal languages”, J. ACM, vol. 35, pp. 324–344, 1988.
Buntrock, G. and Lorys, K., “On growing context-sensitive languages”, Proc. 19th ICALP, Lecture Notes in Computer Science (W. Kuich, ed.), vol. 623, Springer-Verlag, pp. 77–88, 1992.
Book, R.V. and F. Otto, String-rewriting systems, Texts and Monograps in Computer Science, Springer-Verlag, 1993.
Buntrock, G., “Growing context-sensitive languages and automata”, Preprint-Reihe, Nr. 69, Inst, für Informatik, Universität Würzburg, 1993.
Buntrock, G. and Loryś, K., “The variable membership problem: succinctness versus complexity”, Proc. llth STA CS, Lecture Notes in Computer Science (P. Enjalbert, E.W. Mayr and K.W. Wagner, eds.), vol. 775, Springer-Verlag, pp. 595–606, 1994.
Buntrock, G., Wachsend kontextsensitive Sprachen, Habilitationsschrift, Fakultät für Mathematik und Informatik, Universität Würzburg. 1996.
Buntrock, G. and F. Otto, “Growing context-sensitive languages and Church-Rosser languages”, Inf. and Computation, vol. 141, pp. 1–36, 1998.
Niemann, G. and F. Otto, “The Church-Rosser languages are the deterministic variants of the growing context-sensitive languages”, Proc. Foundations of Software Science and Computation Structures, Lecture Notes in Computer Science (M. Nivat, ed.), vol. 1378, Springer-Verlag, pp. 243–257, 1998.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
McNaughton, R. (1999). An Insertion into the Chomsky Hierarchy?. In: Karhumäki, J., Maurer, H., Păun, G., Rozenberg, G. (eds) Jewels are Forever. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60207-8_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-60207-8_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64304-0
Online ISBN: 978-3-642-60207-8
eBook Packages: Springer Book Archive