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Semi-linear Parikh Images of Regular Expressions via Reduction

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Mathematical Foundations of Computer Science 2010 (MFCS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6281))

Abstract

A reduction system for regular expressions is presented. For a regular expression t, the reduction system is proved to terminate in a state where the most-reduced expression readily yields a semi-linear representation for the Parikh image of the language of t.

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References

  1. Aceto, L., Ésik, Z., Ingólfsdóttir, A.: A fully equational proof of Parikh’s theorem. ITA 36(2), 129–153 (2002)

    MATH  Google Scholar 

  2. Blattner, M., Latteux, M.: Parikh-bounded languages. In: Even, S., Kariv, O. (eds.) ICALP 1981. LNCS, vol. 115, pp. 316–323. Springer, Heidelberg (1981)

    Google Scholar 

  3. Delgado, M.: Commutative images of rational languages and the Abelian kernel of a monoid. ITA 35(5), 419–435 (2001)

    MATH  MathSciNet  Google Scholar 

  4. Goldstine, J.: A simplified proof of Parikh’s theorem. Discrete Math. 19, 235–239 (1977)

    Article  MathSciNet  Google Scholar 

  5. Ibarra, O., Kim, C.: A useful device for showing the solvability of some decision problems. In: STOC 1976, pp. 135–140. ACM, New York (1976)

    Chapter  Google Scholar 

  6. Parikh, R.: On context-free languages. J. ACM 13(4), 570–581 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  7. Pilling, D.: Commutative regular equations and Parikh’s theorem. J. London Math. Soc. 6, 633–666 (1973)

    Article  MathSciNet  Google Scholar 

  8. Terese: Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  9. Verma, K.N., Seidl, H., Schwentick, T.: On the complexity of equational Horn clauses. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 337–352. Springer, Heidelberg (2005)

    Google Scholar 

  10. Xie, G., Li, C., Deng, Z.: Linear reachability problems and minimal solutions to linear Diophantine equation systems. TCS 328, 203–219 (2004)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Universität Konstanz,  

    Bahareh Badban

  2. ETH Zürich,  

    Mohammad Torabi Dashti

Authors
  1. Bahareh Badban
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  2. Mohammad Torabi Dashti
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Editor information

Editors and Affiliations

  1. Falculty of Informatics, Masaryk University, Botanicka 68a, 602 00, Brno, Czech Republic

    Petr Hliněný

  2. Faculty of Informatics, Masaryk University, Botanicka 68a, 602 00, Brno, Czech Republic

    Antonín Kučera

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© 2010 Springer-Verlag Berlin Heidelberg

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Badban, B., Torabi Dashti, M. (2010). Semi-linear Parikh Images of Regular Expressions via Reduction. In: Hliněný, P., Kučera, A. (eds) Mathematical Foundations of Computer Science 2010. MFCS 2010. Lecture Notes in Computer Science, vol 6281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15155-2_57

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  • DOI: https://doi.org/10.1007/978-3-642-15155-2_57

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15154-5

  • Online ISBN: 978-3-642-15155-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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