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Regular Expressions with Numerical Constraints and Automata with Counters

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Theoretical Aspects of Computing - ICTAC 2009 (ICTAC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5684))

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Abstract

Regular expressions with numerical constraints are an extension of regular expressions, allowing to bound numerically the number of times that a subexpression should be matched. Expressions in this extension describe the same languages as the usual regular expressions, but are exponentially more succinct.

We define a class of finite automata with counters and a deterministic subclass of these. Deterministic finite automata with counters can recognize words in linear time. Furthermore, we describe a subclass of the regular expressions with numerical constraints, a polynomial-time test for this subclass, and a polynomial-time construction of deterministic finite automata with counters from expressions in the subclass.

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References

  1. The Open Group: The Open Group Base Specifications Issue 6, IEEE Std 1003.1. 2 edn. (1997)

    Google Scholar 

  2. GNU: GNU grep manual

    Google Scholar 

  3. Fallside, D.C.: XML Schema part 0: Primer, W3C recommendation. Technical report, World Wide Web Consortium (W3C) (2001)

    Google Scholar 

  4. Kilpeläinen, P., Tuhkanen, R.: Regular expressions with numerical occurrence indicators - preliminary results. In: Kilpeläinen, P., Päivinen, N. (eds.) SPLST, pp. 163–173. University of Kuopio, Department of Computer Science (2003)

    Google Scholar 

  5. Brüggemann-Klein, A.: Regular expressions into finite automata. Theoretical Computer Science 120(2), 197–213 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gelade, W., Martens, W., Neven, F.: Optimizing schema languages for XML: Numerical constraints and interleaving. In: Schwentick, T., Suciu, D. (eds.) ICDT 2007. LNCS, vol. 4353, pp. 269–283. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Kilpeläinen, P., Tuhkanen, R.: One-unambiguity of regular expressions with numeric occurrence indicators. Information and Computation 205(6), 890–916 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bezem, M., Klop, J.W., de Vrijer, R. (eds.): Term Rewriting Systems. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  9. Brüggemann-Klein, A., Wood, D.: One-unambiguous regular languages. Information and Computation 140(2), 229–253 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  10. Glushkov, V.M.: The abstract theory of automata. Russian Mathematical Surveys 16(5), 1–53 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading (1979)

    MATH  Google Scholar 

  12. Kleene, S.C.: Representation of events in nerve sets and finite automata. Automata Studies, 3–41 (1956)

    Google Scholar 

  13. Kilpeläinen, P., Tuhkanen, R.: Towards efficient implementation of XML schema content models. In: Munson, E.V., Vion-Dury, J.Y. (eds.) ACM Symposium on Document Engineering, pp. 239–241. ACM, New York (2004)

    Google Scholar 

  14. Ghelli, G., Colazzo, D., Sartiani, C.: Linear time membership in a class of regular expressions with interleaving and counting. In: Shanahan, J.G., Amer-Yahia, S., Manolescu, I., Zhang, Y., Evans, D.A., Kolcz, A., Choi, K.S., Chowdhury, A. (eds.) CIKM, pp. 389–398. ACM, New York (2008)

    Chapter  Google Scholar 

  15. Dal-Zilio, S., Lugiez, D.: Xml schema, tree logic and sheaves automata. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 246–263. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  16. Laurikari, V.: NFAs with tagged transitions, their conversion to deterministic automata and application to regular expressions. In: SPIRE, pp. 181–187 (2000)

    Google Scholar 

  17. Brüggemann-Klein, A.: Regular expressions into finite automata. In: Simon, I. (ed.) LATIN 1992. LNCS, vol. 583, pp. 87–98. Springer, Heidelberg (1992)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, Norway

    Dag Hovland

Authors
  1. Dag Hovland
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Editor information

Editors and Affiliations

  1. Institut für Informatik, TU München, Boltzmannstr. 3, 85748, Garching, Germany

    Martin Leucker

  2. School of Computer Science and Engineering, University of New South Wales, Sydney, Australia

    Carroll Morgan

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Hovland, D. (2009). Regular Expressions with Numerical Constraints and Automata with Counters. In: Leucker, M., Morgan, C. (eds) Theoretical Aspects of Computing - ICTAC 2009. ICTAC 2009. Lecture Notes in Computer Science, vol 5684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03466-4_15

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  • DOI: https://doi.org/10.1007/978-3-642-03466-4_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03465-7

  • Online ISBN: 978-3-642-03466-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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