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Regular and Context-Free Pattern Languages over Small Alphabets

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Developments in Language Theory (DLT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7410))

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Abstract

Pattern languages are generalisations of the copy language, which is a standard textbook example of a context-sensitive and non-context-free language. In this work, we investigate a counter-intuitive phenomenon: with respect to alphabets of size 2 and 3, pattern languages can be regular or context-free in an unexpected way. For this regularity and context-freeness of pattern languages, we give several sufficient and necessary conditions and improve known results.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Bader, C., Moura, A.: A generalization of Ogden’s Lemma. Journal of the Association for Computing Machinery 29, 404–407 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  3. Câmpeanu, C., Salomaa, K., Yu, S.: A formal study of practical regular expressions. International Journal of Foundations of Computer Science 14, 1007–1018 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Freydenberger, D.D., Reidenbach, D.: Bad news on decision problems for patterns. Information and Computation 208, 83–96 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Freydenberger, D.D., Reidenbach, D., Schneider, J.C.: Unambiguous morphic images of strings. International Journal of Foundations of Computer Science 17, 601–628 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Harju, T., Karhumäki, J.: Morphisms. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, ch. 7, pp. 439–510. Springer (1997)

    Google Scholar 

  7. Jain, S., Ong, Y.S., Stephan, F.: Regular patterns, regular languages and context-free languages. Information Processing Letters 110, 1114–1119 (2010)

    Article  MathSciNet  Google Scholar 

  8. Jiang, T., Kinber, E., Salomaa, A., Salomaa, K., Yu, S.: Pattern languages with and without erasing. International Journal of Computer Mathematics 50, 147–163 (1994)

    Article  MATH  Google Scholar 

  9. Lange, S., Wiehagen, R.: Polynomial-time inference of arbitrary pattern languages. New Generation Computing 8, 361–370 (1991)

    Article  MATH  Google Scholar 

  10. Mateescu, A., Salomaa, A.: Finite degrees of ambiguity in pattern languages. RAIRO Informatique théoretique et Applications 28, 233–253 (1994)

    MathSciNet  MATH  Google Scholar 

  11. Mateescu, A., Salomaa, A.: Patterns. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, pp. 230–242. Springer (1997)

    Google Scholar 

  12. Ng, Y.K., Shinohara, T.: Developments from enquiries into the learnability of the pattern languages from positive data. Theoretical Computer Science 397, 150–165 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Reidenbach, D.: The Ambiguity of Morphisms in Free Monoids and its Impact on Algorithmic Properties of Pattern Languages. PhD thesis, Fachbereich Informatik, Technische Universität Kaiserslautern. Logos Verlag, Berlin (2006)

    Google Scholar 

  14. Reidenbach, D.: Discontinuities in pattern inference. Theoretical Computer Science 397, 166–193 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Rossmanith, P., Zeugmann, T.: Stochastic finite learning of the pattern languages. Machine Learning 44, 67–91 (2001)

    Article  MATH  Google Scholar 

  16. Shinohara, T.: Polynomial Time Inference of Extended Regular Pattern Languages. In: Goto, E., Furukawa, K., Nakajima, R., Nakata, I., Yonezawa, A. (eds.) RIMS 1982. LNCS, vol. 147, pp. 115–127. Springer, Heidelberg (1983)

    Chapter  Google Scholar 

  17. Shinohara, T.: Polynomial time inference of pattern languages and its application. In: Proc. 7th IBM MFCS, pp. 191–209 (1982)

    Google Scholar 

  18. Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, ch. 2, pp. 41–110. Springer (1997)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom

    Daniel Reidenbach & Markus L. Schmid

Authors
  1. Daniel Reidenbach
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  2. Markus L. Schmid
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Editors and Affiliations

  1. Deptartment of Electrical Engineering, National Taiwan University, 106, Taipei, Taiwan

    Hsu-Chun Yen

  2. Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA

    Oscar H. Ibarra

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Reidenbach, D., Schmid, M.L. (2012). Regular and Context-Free Pattern Languages over Small Alphabets. In: Yen, HC., Ibarra, O.H. (eds) Developments in Language Theory. DLT 2012. Lecture Notes in Computer Science, vol 7410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31653-1_13

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  • DOI: https://doi.org/10.1007/978-3-642-31653-1_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31652-4

  • Online ISBN: 978-3-642-31653-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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