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Finding a One-Variable Pattern from Incomplete Data

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Algorithmic Learning Theory (ALT 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1501))

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Abstract

The present paper deals with the problem of finding a consistent one-variable pattern from incomplete positive and negative examples. The studied problems are called an extension e, a consistent extension ce and a robust extension re, respectively. Problem e corresponds to the ordinary problem to decide whether there exists a one-variable pattern that is consistent with the given positive and negative examples. As for the other problems, an example string is allowed to contain some unsettled symbols that can potentially match with every constant symbol. For the problem ce, one has to decide whether there exists a suitable assignment for these unsettled symbols as well as a one-variable pattern consistent with the examples with respect to the assignment chosen. Problem re is the universal version of problem ce, i.e., now one has to decide whether there exists a one-variable pattern that is consistent with the examples under every assignment for the unsettled symbols. The decision problems defined are closely connected to the learnability of one-variable pattern languages from positive and negative examples. The computational complexity of the decision problems defined above is studied. In particular, it shown that re is NP-complete.

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References

  1. D. Angluin. Finding patterns common to a set of strings. Journal of Computer and System Sciences 21:46–62, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Arikawa, S. Miyano, A. Shinohara, S. Kuhara, Y. Mukouchi and T. Shinohara. A machine discovery from amino acid sequences by decision trees over regular patterns. New Generation Computing 11:361–375, 1993.

    Article  MATH  Google Scholar 

  3. E. Boros, T. Ibaraki and K. Makino. Monotone extensions of Boolean data sets. In Proc. 8th International Workshop on Algorithmic Learning Theory, Lecture Notes in Artificial Intelligence 1316, pp. 161–175, Berlin, 1997. Springer-Verlag.

    Google Scholar 

  4. T. Erlebach, P. Rossmanith, H. Stadtherr, A. Steger and T. Zeugmann. Learning one-variable pattern languages very eciently on average, in parallel, and by asking queries. In Proc. 8th International Workshop on Algorithmic Learning Theory, Lecture Notes in Artificial Intelligence 1316, pp. 260–276, Berlin, 1997. Springer-Verlag.

    Google Scholar 

  5. M.R. Garey and D.S. Johnson. Computers and Intractability. W.H. Freeman and company, 1983.

    Google Scholar 

  6. M.E. Gold. Language identication in the limit. Information and Control 10:447–474.

    Google Scholar 

  7. J.E. Hopcroft and J.D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley Publ., 1979.

    Google Scholar 

  8. T. Jiang, A. Salomaa, K. Salomaa and S. Yu. Inclusion is undecidable for pattern languages. In Proc. 20th ICALP, Lecture Notes in Computer Science 700, pp. 301–312, Berlin, 1993. Springer-Verlag.

    Google Scholar 

  9. M.J. Kearns and U.J. Vazirani. An Introduction to Computational Learning Theory. The MIT Press, Cambridge, MA 1994.

    Google Scholar 

  10. C.H. Papadimitriou. Computational complexity. Addison-Wesley Publ., 1994.

    Google Scholar 

  11. R. Reischuk and T. Zeugmann. Learning One-variable pattern languages in linear average time. In Proc. 11st Ann. Conference on Computational Learning Theory, 1998, to appear.

    Google Scholar 

  12. R.E. Schapire. Pattern languages are not learnable. In M.A. Fulk and J. Case, editors, Proc. 3rd Annual ACM Workshop on Computational Learning Theory, pp. 122–129, 1990. Morgan Kaufmann Publishers Inc., San Mateo.

    Google Scholar 

  13. T. Shinohara and S. Arikawa. Pattern inference. In Algorithmic Learning for Knowledge-Based Systems, Lecture Notes in Artificial Intelligence 961, pp. 259–291, Berlin, 1995. Springer-Verlag.

    Google Scholar 

  14. R. Wiehagen and T. Zeugmann. Ignoring data may be the only way to learn eciently. Journal of Experimental and Theoretical Artificial Intelligence 6:131–144, 1994.

    Article  MATH  Google Scholar 

  15. T. Zeugmann and S. Lange. A guided tour across the boundaries of learning recursive languages. In Algorithmic Learning for Knowledge-Based Systems, (K.P. Jantke and S. Lange, Eds.), Lecture Notes in Artificial Intelligence 961, pp. 193–262, Berlin, 1995. Springer-Verlag.

    Google Scholar 

  16. T. Zeugmann, S. Lange and S. Kapur. Characterizations of monotonic and dual monotonic language learning. Information and Computation 120(2):155–173.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Informatics, Kyushu University, Fukuoka, 812-8581, Japan

    Hiroshi Sakamoto

Authors
  1. Hiroshi Sakamoto
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Editor information

Editors and Affiliations

  1. AG Künstliche Intelligenz - Expertensysteme, UniversitÄt Kaiserslautern, Postfach 3049, D-67653, Kaiserslautern, Germany

    Michael M. Richter

  2. Department of Computer Science, University of Maryland, College Park, MD, 20742, USA

    Carl H. Smith

  3. AG Algorithmischesn Lernen, UniversitÄt Kaiserslautern, Postfach 3049, D-67653, Kaiserslautern, Germany

    Rolf Wiehagen

  4. Graduate School of Information Science and Electrical Engineering Department of Informatics, Kyushu University, Kassuga, 816-8580, Japan

    Thomas Zeugmann

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© 1998 Springer-Verlag Berlin Heidelberg

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Sakamoto, H. (1998). Finding a One-Variable Pattern from Incomplete Data. In: Richter, M.M., Smith, C.H., Wiehagen, R., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 1998. Lecture Notes in Computer Science(), vol 1501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49730-7_18

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  • DOI: https://doi.org/10.1007/3-540-49730-7_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65013-3

  • Online ISBN: 978-3-540-49730-1

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