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Inclusion Test Algorithms for One-Unambiguous Regular Expressions

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Theoretical Aspects of Computing - ICTAC 2008 (ICTAC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5160))

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Abstract

One-unambiguous regular expressions are used in DTD. It is known that inclusion for one-unambiguous regular expressions is in PTIME. However, there has been no study on algorithms for the inclusion. In this paper we present algorithms for checking inclusion of one-unambiguous regular expressions. A classical way is based on automata, following which one algorithm is provided and improvements are given. The other algorithm is based on derivatives, utilizing a property introduced here that the number of derivatives of a one-unambiguous regular expression is finite. We conducted preliminary experiments by implementing typechecking of XML using the algorithms. The results show that typechecking using the new algorithms is more efficient than the typechecking used for XDuce.

Work supported by the National Natural Science Foundation of China under Grants Nos. 60573013, 60721061.

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References

  1. Antimirov, V.: Partial derivatives of regular expressions and finite automaton constructions. Theoretical Computer Science 155, 291–319 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Antimirov, V.: Rewriting regular inequalities. In: FCT 1995. LNCS, vol. 965, pp. 116–125. Springer, Heidelberg (1995)

    Google Scholar 

  3. Benzaken, V., Castagna, G., Frisch, A.: CDuce: An XML centric general-purpose language. In: ACM SIGPLAN International Conference on Functional Programming (ICFP), Uppsala, Sweden, pp. 51–63 (2003)

    Google Scholar 

  4. Bex, G.J., Neven, F., Bussche, J.V.: DTDs versus XML schema: a practical study. In: WebDB 2004, pp. 79–84 (2004)

    Google Scholar 

  5. Bray, T., et al.: XML 1.1, W3C Recommendation, 2nd edn. (2006)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Bruggemann-Klein, A., Wood, D.: One-unambiguous regular languages. Information and Computation 142(2), 182–206 (1998)

    Article  MathSciNet  Google Scholar 

  8. Brzozowski, J.A.: Derivatives of regular expressions. J. ACM 11(4), 481–494 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  9. Chen, H.: Derivatives and automata of one-unambiguous regular expressions (submitted, 2008)

    Google Scholar 

  10. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, Cambridge (2001)

    MATH  Google Scholar 

  11. 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. Springer, Heidelberg (2006)

    Google Scholar 

  12. Ghelli, G., Colazzo, D., Sartiani, C.: Efficient inclusion for a class of XML types with interleaving and counting. In: Arenas, M., Schwartzbach, M.I. (eds.) DBPL 2007. LNCS, vol. 4797, pp. 231–245. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  14. Hosoya, H., Pierce, B.: XDuce: a statically typed XML processing language. ACM Transactions on Internet Technology 3(2), 117–148 (2003)

    Article  Google Scholar 

  15. Kilpelainen, P., Tuhkanen, R.: Regular expressions with numerical occurrence indicators - preliminary results. In: SPLST 2003, pp. 163–173 (2003)

    Google Scholar 

  16. Martens, W., Neven, F., Schwentick, T.: Complexity of decision problems for simple regular expressions. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 889–900. Springer, Berlin (2004)

    Google Scholar 

  17. Mayer, A.J., Stockmeyer, L.J.: Word problems - this time with interleaving. Information and Computation 115(2), 293–311 (1994)

    Article  MathSciNet  Google Scholar 

  18. McNaughton, R., Yamada, H.: Regular expressions and state graphs for automata. IEEE Trans. on Electronic Computers 9(1), 39–47 (1960)

    Article  Google Scholar 

  19. Sperberg-McQueen, C.M., Thompson, H.: XML Schema, http://www.w3.org/XML/Schema

  20. Stockmeyer, L.J., Meyer, A.R.: Word problems requiring exponential time: Preliminary report. In: STOC 1973, pp. 1–9. ACM Press, New York (1973)

    Chapter  Google Scholar 

  21. Suzuki, N.: An edit operation-based approach to the inclusion problem for DTDs. In: Adams, C., Miri, A., Wiener, M. (eds.) SAC 2007. LNCS, vol. 4876, pp. 482–488. Springer, Heidelberg (2007)

    Google Scholar 

  22. Yu, S.: Regular Languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. I, pp. 41–110. Springer, Berlin (1997)

    Google Scholar 

  23. XDuce Webpage, http://xduce.sourceforge.net/

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Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, 100080, China

    Haiming Chen & Lei Chen

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  1. Haiming Chen
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  2. Lei Chen
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John S. Fitzgerald Anne E. Haxthausen Husnu Yenigun

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Chen, H., Chen, L. (2008). Inclusion Test Algorithms for One-Unambiguous Regular Expressions. In: Fitzgerald, J.S., Haxthausen, A.E., Yenigun, H. (eds) Theoretical Aspects of Computing - ICTAC 2008. ICTAC 2008. Lecture Notes in Computer Science, vol 5160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85762-4_7

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  • DOI: https://doi.org/10.1007/978-3-540-85762-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85761-7

  • Online ISBN: 978-3-540-85762-4

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