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On the Commutative Equivalence of Bounded Semi-linear Codes

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11682))

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Abstract

The problem of the commutative equivalence of semigroups generated by semi-linear languages is studied. In particular conditions ensuring that the Kleene closure of a bounded semi-linear code is commutatively equivalent to a regular language are investigated.

The research of F. D’Alessandro was partially supported by TUBITAK Project 2221 (Scientific and Technological Research Council of Turkey) and by the National Group for Algebraic and Geometric Structures, and their Applications (GNSAGA–INdAM).

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References

  1. Béal, M.-P., Perrin, D.: On the generating sequences of regular languages on \(k\) symbols. J. ACM 50, 955–980 (2003)

    Article  MathSciNet  Google Scholar 

  2. Boasson, L., Restivo, A.: Une Caractérisation des Langages Algébriques Bornés. ITA 11, 203–205 (1977)

    MATH  Google Scholar 

  3. Baron, G., Kuich, W.: The characterization of nonexpansive grammars by rational power series. Inf. Control 48, 109–118 (1981)

    Article  MathSciNet  Google Scholar 

  4. Berstel, J., Perrin, D., Reutenauer, C.: Codes and Automata Encyclopedia of Mathematics and its Applications, vol. 129. Cambridge University Press, Cambridge (2009)

    Google Scholar 

  5. Bridson, M.R., Gilman, R.H.: Context-free languages of sub-exponential growth. J. Comput. Syst. Sci. 64, 308–310 (1999)

    Article  MathSciNet  Google Scholar 

  6. Carpi, A., D’Alessandro, F.: On the commutative equivalence of context-free languages. In: Hoshi, M., Seki, S. (eds.) DLT 2018. LNCS, vol. 11088, pp. 169–181. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98654-8_14

    Chapter  Google Scholar 

  7. Choffrut, C., D’Alessandro, F., Varricchio, S.: On bounded rational trace languages. Theory Comput. Syst. 46, 351–369 (2010)

    Article  MathSciNet  Google Scholar 

  8. Chomsky, N., Schützenberger, M.-P.: The algebraic theory of context-free languages. In: Braffort, P., Hirschberg, D. (eds.) Computer Programming and Formal Systems, pp. 118–161. North Holland Publishing Company, Amsterdam (1963)

    Chapter  Google Scholar 

  9. D’Alessandro, F., Intrigila, B., Varricchio, S.: The Parikh counting functions of sparse context-free languages are quasi-polynomials. Theoret. Comput. Sci. 410, 5158–5181 (2009)

    Article  MathSciNet  Google Scholar 

  10. D’Alessandro, F., Intrigila, B., Varricchio, S.: Quasi-polynomials, linear Diophantine equations and semi-linear sets. Theoret. Comput. Sci. 416, 1–16 (2012)

    Article  MathSciNet  Google Scholar 

  11. D’Alessandro, F., Intrigila, B.: On the commutative equivalence of bounded context-free and regular languages: the code case. Theoret. Comput. Sci. 562, 304–319 (2015)

    Article  MathSciNet  Google Scholar 

  12. D’Alessandro, F., Intrigila, B.: On the commutative equivalence of semi-linear sets of \(\mathbb{N}^{k}\). Theoret. Comput. Sci. 562, 476–495 (2015)

    Article  MathSciNet  Google Scholar 

  13. D’Alessandro, F., Intrigila, B.: On the commutative equivalence of bounded context-free and regular languages: the semi-linear case. Theoret. Comput. Sci. 572, 1–24 (2015)

    Article  MathSciNet  Google Scholar 

  14. D’Alessandro, F., Ibarra, O.H., McQuillan, I.: On finite-index indexed grammars and their restrictions. In: Drewes, F., Martín-Vide, C., Truthe, B. (eds.) LATA 2017. LNCS, vol. 10168, pp. 287–298. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-53733-7_21

    Chapter  MATH  Google Scholar 

  15. de Luca, A., Varricchio, S.: Finiteness and Regularity in Semigroups and Formal Languages. Springer, Berlin (1999). https://doi.org/10.1007/978-3-642-59849-4

    Book  MATH  Google Scholar 

  16. Eilenberg, S., Schützenberger, M.-P.: Rational sets in commutative monoids. J. Algebra 13, 173–191 (1969)

    Article  MathSciNet  Google Scholar 

  17. Flajolet, P.: Analytic models and ambiguity of context-free languages. Theoret. Comput. Sci. 49, 283–309 (1987)

    Article  MathSciNet  Google Scholar 

  18. Ginsburg, S., Spanier, E.H.: Semigroups, presburger formulas, and languages. Pacific J. Math. 16, 285–296 (1966)

    Article  MathSciNet  Google Scholar 

  19. Ginsburg, S.: The Mathematical Theory of Context-Free Languages. Mc Graw-Hill, New York (1966)

    MATH  Google Scholar 

  20. Gross, M.: Inherent ambiguity of minimal linear grammars. Inf. Control 7, 366–368 (1964)

    Article  MathSciNet  Google Scholar 

  21. Honkala, J.: Decision problems concerning thinness and slenderness of formal languages. Acta Inf. 35, 625–636 (1998)

    Article  MathSciNet  Google Scholar 

  22. Honkala, J.: On Parikh slender context-free languages. Theoret. Comput. Sci. 255, 667–677 (2001)

    Article  MathSciNet  Google Scholar 

  23. H.Ibarra, O., Ravikumar, B.: On sparseness, ambiguity and other decision problems for acceptors and transducers. In: Monien, B., Vidal-Naquet, G. (eds.) STACS 1986. LNCS, vol. 210, pp. 171–179. Springer, Heidelberg (1986). https://doi.org/10.1007/3-540-16078-7_74

    Chapter  Google Scholar 

  24. Ibarra, O.H., McQuillan, I., Ravikumar, B.: On counting functions of languages. In: Hoshi, M., Seki, S. (eds.) DLT 2018. LNCS, vol. 11088, pp. 429–440. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98654-8_35

    Chapter  Google Scholar 

  25. Ilie, L., Rozenberg, G., Salomaa, A.: A characterization of poly-slender context-free languages. RAIRO Inform. Théor. Appl. 34, 77–86 (2000)

    Article  MathSciNet  Google Scholar 

  26. Incitti, R.: The growth function of context-free languages. Theoret. Comput. Sci. 255, 601–605 (2001)

    Article  MathSciNet  Google Scholar 

  27. Latteux, M., Thierrin, G.: On bounded context-free languages. Elektron. Inform. Verarb. u. Kybern. 20, 3–8 (1984)

    MathSciNet  MATH  Google Scholar 

  28. Restivo, A.: A characterization of bounded regular sets. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, pp. 239–244. Springer, Heidelberg (1975). https://doi.org/10.1007/3-540-07407-4_26

    Chapter  Google Scholar 

  29. Trofimov, V.I.: Growth functions of some classes of languages. Kibernetika (Kiev), (6), 9–12, 149 (1981)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, via Vanvitelli 1, 06123, Perugia, Italy

    Arturo Carpi

  2. Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185, Rome, Italy

    Flavio D’Alessandro

  3. Department of Mathematics, Boğaziçi University, 34342, Bebek, Istanbul, Turkey

    Flavio D’Alessandro

Authors
  1. Arturo Carpi
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  2. Flavio D’Alessandro
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Correspondence to Flavio D’Alessandro .

Editor information

Editors and Affiliations

  1. Loughborough University, Loughborough, UK

    Robert Mercaş

  2. Loughborough University, Loughborough, UK

    Daniel Reidenbach

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Carpi, A., D’Alessandro, F. (2019). On the Commutative Equivalence of Bounded Semi-linear Codes. In: Mercaş, R., Reidenbach, D. (eds) Combinatorics on Words. WORDS 2019. Lecture Notes in Computer Science(), vol 11682. Springer, Cham. https://doi.org/10.1007/978-3-030-28796-2_9

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  • DOI: https://doi.org/10.1007/978-3-030-28796-2_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-28795-5

  • Online ISBN: 978-3-030-28796-2

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