Abstract
On the one hand, the inclusion problem for nonerasing and erasing pattern languages is undecidable; see [JSSY95]. On the other hand, the language equivalence problem for NE-pattern languages is trivially decidable (see [Ang80a]) but the question of whether the same holds for E-pattern languages is still open. It has been conjectured by Jiang et al. [JSSY95] that the language equivalence problem for E-pattern languages is also decidable. In this paper, we introduce a new normal form for patterns and show, using the normal form, that the language equivalence problem for E-pattern languages is decidable in many special cases. We conjecture that our normal form procedure decides the problem in the general case, too. If the conjecture holds true, then the normal form is the shortest pattern generating a given E-pattern language.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
D. Angluin. Finding patterns common to a set of strings. Journal of Computer and System Sciences 21, pages 46–62, 1980.
D. Angluin. Inductive inference of formal languages from positive data. Information and Control 45, pages 117–135, 1980.
G. Dányi and Z. Fülöp. A note on the equivalence problem of E-patterns. Information Processing Letters 57, pages 125–128, 1996.
O. Ibarra and T. Jiang. Learning regular languages from counterexamples. Journal of Computer and System Sciences 43, pages 299–316, 1991.
[JKS+94] T. Jiang, E. Kinber, A. Salomaa, K. Salomaa, and S. Yu. Pattern languages with and without erasing. Intern. J. Computer Math. 50, pages 147–163, 1994.
T. Jiang, A. Salomaa, K. Salomaa, and S. Yu. Decision problems for patterns. Journal of Computer and System Sciences 50, pages 53–63, 1995.
P. Kilpeläinen, H. Mannila, and E. Ukkonen. MDL learning of unions of simple pattern languages from positive examples. In Proceedings of the 2nd European Conference on Computational Learning Theory, pages 252–260. Lecture Notes in Computer Science 904, Berlin: Springer Verlag, 1995.
E. Ohlebusch and E. Ukkonen. On the the equivalence problem for E-pattern languages. Report 95-04, Forschungsberichte der Technischen Fakultät, Abteilung Informationstechnik, Universität Bielefeld, 1995.
A. Salomaa. Patterns. Bulletin of the European Association for Theoretical Computer Science 54, pages 194–206, 1994.
A. Salomaa. Return to patterns. Bulletin of the European Association for Theoretical Computer Science 55, pages 144–155, 1995.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ohlebusch, E., Ukkonen, E. (1996). On the equivalence problem for E-pattern languages. In: Penczek, W., Szałas, A. (eds) Mathematical Foundations of Computer Science 1996. MFCS 1996. Lecture Notes in Computer Science, vol 1113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61550-4_170
Download citation
DOI: https://doi.org/10.1007/3-540-61550-4_170
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61550-7
Online ISBN: 978-3-540-70597-0
eBook Packages: Springer Book Archive