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On the word problem for syntactic monoids of piecewise testable languages

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Abstract

Piecewise testable languages are widely studied area in the theory of automata. We analyze the algebraic properties of these languages via their syntactic monoids. In this paper a normal form is presented for 2- and 3-piecewise testable languages and a log-asymptotic estimate is given for the number of words over these monoids.

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References

  1. Blanchet-Sadri, F.: Games equations and dot-depth hierarchy. Comput. Math. Appl. 18, 809–822 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Blanchet-Sadri, F.: Equations and monoids varieties of dot-depth one and two. Theor. Comput. Sci. 123, 239–258 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Pin, J.E.: Finite semigroups and recognizable languages: an introduction. In: Semigroups, Formal Languages and Groups, York, 1993. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 466, pp. 1–32. Kluwer Academic, Dordrecht (1995)

    Google Scholar 

  4. Pin, J.E.: Varieties of Formal Languages. North Oxford Academic/Plenum, London/New York (1986)

    Book  MATH  Google Scholar 

  5. Stern, J.: Complexity of some problems from the theory of automata. Inf. Control 66, 163–176 (1985)

    Article  MATH  Google Scholar 

  6. Simon, I.: Piecewise testable events. In: Proc. 2nd GI Conf. Lect. Notes in Comput. Sci., vol. 33, pp. 214–222 (1975)

    Google Scholar 

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Authors and Affiliations

  1. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720, Szeged, Hungary

    Kamilla Kátai-Urbán

  2. Department of Algebra and Number Theory, Eötvös Loránd University, 1117, Budapest, Pázmány Péter sétány 1/c, Hungary

    Péter Pál Pach, Gabriella Pluhár & Csaba Szabó

  3. Department of Mathematics and Applications, Central European University, 1051, Budapest, Nádor utca 9, Hungary

    András Pongrácz

Authors
  1. Kamilla Kátai-Urbán
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  2. Péter Pál Pach
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  3. Gabriella Pluhár
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  4. András Pongrácz
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  5. Csaba Szabó
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Corresponding author

Correspondence to Kamilla Kátai-Urbán.

Additional information

Communicated by Marcel Jackson.

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Kátai-Urbán, K., Pach, P.P., Pluhár, G. et al. On the word problem for syntactic monoids of piecewise testable languages. Semigroup Forum 84, 323–332 (2012). https://doi.org/10.1007/s00233-011-9357-z

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  • DOI: https://doi.org/10.1007/s00233-011-9357-z

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