Abstract
It has been known since 1962 that the ambiguity problem for context-free grammars is undecidable. Ambiguity in context-free grammars is a recurring problem in language design and parser generation, as well as in applications where grammars are used as models of real-world physical structures.
We observe that there is a simple linguistic characterization of the grammar ambiguity problem, and we show how to exploit this to conservatively approximate the problem based on local regular approximations and grammar unfoldings. As an application, we consider grammars that occur in RNA analysis in bioinformatics, and we demonstrate that our static analysis of context-free grammars is sufficiently precise and efficient to be practically useful.
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
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading (1979)
Knuth, D.E.: On the translation of languages from left to right. Information and Control 8, 607–639 (1965)
Culik II, K., Cohen, R.S.: LR-regular grammars - an extension of LR(k) grammars. Journal of Computer and System Sciences 7(1), 66–96 (1973)
Scott, E., Johnstone, A., Hussein, S.S.: Tomita style generalised parsers. Technical Report CSD-TR-00-A, Royal Holloway, University of London (2000)
Visser, E.: Syntax Definition for Language Prototyping. PhD thesis, University of Amsterdam (1997)
McPeak, S., Necula, G.C.: Elkhound: A fast, practical GLR parser generator. In: Duesterwald, E. (ed.) CC 2004. LNCS, vol. 2985, Springer, Heidelberg (2004)
van den Brand, M., Scheerder, J., Vinju, J.J., Visser, E.: Disambiguation filters for scannerless generalized LR parsers. In: Horspool, R.N. (ed.) CC 2002 and ETAPS 2002. LNCS, vol. 2304, Springer, Heidelberg (2002)
Brabrand, C., Schwartzbach, M.I., Vanggaard, M.: The metafront system: Extensible parsing and transformation. In: LDTA 2003. Proc. 3rd ACM SIGPLAN Workshop on Language Descriptions, Tools and Applications, ACM Press, New York (2003)
Gorn, S.: Detection of generative ambiguities in context-free mechanical languages. Journal of the ACM 10(2), 196–208 (1963)
Cheung, B.S.N., Uzgalis, R.C.: Ambiguity in context-free grammars. In: SAC 1995. Proc. ACM Symposium on Applied Computing, ACM Press, New York (1995)
Schmitz, S.: Conservative ambiguity detection in context-free grammars. In: ICALP 2007. Proc. 34th International Colloquium on Automata, Languages and Programming (2007)
Kuich, W.: Systems of pushdown acceptors and context-free grammars. Elektronische Informationsverarbeitung und Kybernetik 6(2), 95–114 (1970)
Durbin, R., Eddy, S.R., Krogh, A., Mitchison, G.: Biological Sequence Analysis. Cambridge University Press, Cambridge (1998)
Giegerich, R., Meyer, C., Steffen, P.: A discipline of dynamic programming over sequence data. Science of Computer Programming 51(3), 215–263 (2004)
Giegerich, R.: Explaining and controlling ambiguity in dynamic programming. In: Giancarlo, R., Sankoff, D. (eds.) CPM 2000. LNCS, vol. 1848, pp. 46–59. Springer, Heidelberg (2000)
Dowell, R.D., Eddy, S.R.: Evaluation of several lightweight stochastic context-free grammars for RNA secondary structure prediction. BMC Bioinformatics 5(71) (2004)
Brabrand, C., Møller, A., Schwartzbach, M.I.: Dual syntax for XML languages. In: Bierman, G., Koch, C. (eds.) DBPL 2005. LNCS, vol. 3774, Springer, Heidelberg (2005)
Mohri, M., Nederhof, M.J.: 9: Regular Approximation of Context-Free Grammars through Transformation. In: Robustness in Language and Speech Technology, Kluwer Academic Publishers, Dordrecht (2001)
Brabrand, C., Giegerich, R., Møller, A.: Analyzing ambiguity of context-free grammars. Technical Report RS-07-10, BRICS (2007)
Møller, A.: dk.brics.automaton – finite-state automata and regular expressions for Java (2007), http://www.brics.dk/automaton/
Aho, A.V., Ullman, J.D.: The Theory of Parsing, Translation and Compiling, vol. 1: Parsing. Prentice-Hall, Englewood Cliffs (1972)
Reeder, J., Steffen, P., Giegerich, R.: Effective ambiguity checking in biosequence analysis. BMC Bioinformatics 6(153) (2005)
Voss, B., Giegerich, R., Rehmsmeier, M.: Complete probabilistic analysis of RNA shapes. BMC Biology 4(5) (2006)
Reeder, J., Giegerich, R.: A graphical programming system for molecular motif search. In: GPCE 2006. Proc. 5th International Conference on Generative Programming and Component Engineering, pp. 131–140. ACM Press, New York (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brabrand, C., Giegerich, R., Møller, A. (2007). Analyzing Ambiguity of Context-Free Grammars. In: Holub, J., Žďárek, J. (eds) Implementation and Application of Automata. CIAA 2007. Lecture Notes in Computer Science, vol 4783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76336-9_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-76336-9_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76335-2
Online ISBN: 978-3-540-76336-9
eBook Packages: Computer ScienceComputer Science (R0)