Abstract
We prove that the class of context-free languages with polynomially bounded ambiguity (PCFL) is the closure of the class of unambiguous languages ( UCFL) under projections which deletes Parikh bounded symbols only. A symbol a is Parikh bounded in a language L if there is a constant c such that no word of L contains more than c occurrences of a. Furthermore PCFL is closed under the formally stronger operation of Parikh bounded substitution, i.e., a substitution which is the identity for non Parikh bounded symbols. Finally we prove that the closure of UCFL under union and concatenation is a proper subset of PCFL.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J. Berstel. Transductions and context-free languages. Teubner, Stuttgart, 1979.
A. Bertoni, M. Goldwurm, and M. Santini. Random generation and approximate counting of ambiguously described combinatorical structures. In H. Reichel and S. Tison, editors, Proc. STACS 2000, LNCS 1770, pp. 567–580, Berlin-Heidelberg-New York, 2000. Springer.
J. Crestin. Un langage non ambigu dont le carré est d’ambiguité non bornée. In M. Nivat, editor, Automata, Languages and Programming, pp. 377–390. Amsterdam, North-Holland, 1973.
J. C. Earley. An efficient context-free parsing algorithm. PhD thesis, Carnegie-Mellon Uni., 1968.
M. A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, Reading, 1978.
H. Maurer. The existence of context-free languages which are inherently ambiguous of any degree. Research series, Dept. of Mathematics, Uni. of Calgary, 1968.
M. Naji. Grad der Mehrdeutigkeit kontextfreier Grammatiken und Sprachen, 1998. Diplomarbeit, FB Informatik, JWG-Universität Frankfurt/M.
R. J. Parikh. Language-generating devices. In Quarterly Progress Report, volume 60, pp. 199–212. Research Laboratory of Electronics, M. I.T, 1961.
A. Salomaa and M. Soittola. Automata theoretic aspects of formal power series. Springer, 1978.
K. Wich. Kriterien für die Mehrdeutigkeit kontextfreier Grammatiken, 1997. Diplomarbeit, FB Informatik, JWG-Universität Frankfurt/M.
K. Wich. Exponential ambiguity of context-free grammars. In G. Rozenberg and W. Thomas, editors, Proc. DLT, 1999, pp. 125–138. World Scientific, Singapore, 2000.
K. Wich. Sublinear ambiguity. In M. Nielsen and B. Rovan, editors, Proc. MFCS 2000, LNCS 1893, pp. 690–698, Berlin-Heidelberg-New York, 2000. Springer.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wich, K. (2001). Characterization of Context-Free Languages with Polynomially Bounded Ambiguity. In: Sgall, J., Pultr, A., Kolman, P. (eds) Mathematical Foundations of Computer Science 2001. MFCS 2001. Lecture Notes in Computer Science, vol 2136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44683-4_61
Download citation
DOI: https://doi.org/10.1007/3-540-44683-4_61
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42496-3
Online ISBN: 978-3-540-44683-5
eBook Packages: Springer Book Archive