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International Conference on Automated Reasoning with Analytic Tableaux and Related Methods

TABLEAUX 2013: Automated Reasoning with Analytic Tableaux and Related Methods pp 10–12Cite as

A Brief Survey of Verified Decision Procedures for Equivalence of Regular Expressions

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8123))

Abstract

We survey a number of decision procedures for the equivalence of regular expressions that have been formalised with the help of interactive proof assistant over the past few years.

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References

  1. Antimirov, V.: Partial derivatives of regular expressions and finite automaton constructions. Theor. Comput. Sci. 155, 291–319 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Asperti, A.: A compact proof of decidability for regular expression equivalence. In: Beringer, L., Felty, A. (eds.) ITP 2012. LNCS, vol. 7406, pp. 283–298. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  3. Berghofer, S., Reiter, M.: Formalizing the logic-automaton connection. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 147–163. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  4. Braibant, T., Pous, D.: An efficient Coq tactic for deciding Kleene algebras. In: Kaufmann, M., Paulson, L. (eds.) ITP 2010. LNCS, vol. 6172, pp. 163–178. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. Coquand, T., Siles, V.: A decision procedure for regular expression equivalence in type theory. In: Jouannaud, J.-P., Shao, Z. (eds.) CPP 2011. LNCS, vol. 7086, pp. 119–134. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  7. Fischer, S., Huch, F., Wilke, T.: A play on regular expressions. Functional pearl. In: Hudak, P., Weirich, S. (eds.) Proc. Int. Conf. Functional Programming, ICFP 2010, pp. 357–368 (2010)

    Google Scholar 

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

    Article  Google Scholar 

  9. Krauss, A., Nipkow, T.: Proof pearl: Regular expression equivalence and relation algebra. J. Automated Reasoning 49, 95–106 (2012) (published online March 2011)

    Google Scholar 

  10. McNaughton, R., Yamada, H.: Regular expressions and finite state graphs for automata. IRE Trans. on Electronic Comput. EC-9, 38–47 (1960)

    Google Scholar 

  11. Moreira, N., Pereira, D., de Sousa, S.M.: Deciding regular expressions (in-)equivalence in Coq. In: Kahl, W., Griffin, T.G. (eds.) RAMiCS 2012. LNCS, vol. 7560, pp. 98–113. Springer, Heidelberg (2012)

    Google Scholar 

  12. Moreira, N., Pereira, D., de Sousa, S.M.: Mechanization of an algorithm for deciding KAT terms equivalence. Tech. Rep. DCC-2012-04, Universidade do Porto (2012)

    Google Scholar 

  13. Owens, S., Reppy, J.H., Turon, A.: Regular-expression derivatives re-examined. J. Functional Programming 19, 173–190 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  14. Traytel, D., Nipkow, T.: A verified decision procedure for MSO on words based on derivatives of regular expressions. In: Proc. Int. Conf. Functional Programming, ICFP 2013 (2013)

    Google Scholar 

  15. Wu, C., Zhang, X., Urban, C.: A formalisation of the Myhill-Nerode theorem based on regular expressions (Proof pearl). In: van Eekelen, M., Geuvers, H., Schmaltz, J., Wiedijk, F. (eds.) ITP 2011. LNCS, vol. 6898, pp. 341–356. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Germany

    Tobias Nipkow & Maximilian Haslbeck

Authors
  1. Tobias Nipkow
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  2. Maximilian Haslbeck
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Editor information

Editors and Affiliations

  1. LORIA UMR CNRS 7503, Université de Lorraine, Campus Scientifique, BP 239, 54506, Vandœuvre-lès-Nancy, France

    Didier Galmiche

  2. LORIA – CNRS, UHP Nancy, Campus Scientifique, BP 239, 54 506, Vandœuvre-lès-Nancy, France

    Dominique Larchey-Wendling

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Nipkow, T., Haslbeck, M. (2013). A Brief Survey of Verified Decision Procedures for Equivalence of Regular Expressions. In: Galmiche, D., Larchey-Wendling, D. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2013. Lecture Notes in Computer Science(), vol 8123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40537-2_3

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  • DOI: https://doi.org/10.1007/978-3-642-40537-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40536-5

  • Online ISBN: 978-3-642-40537-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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