Abstract
In this paper, we study the lattice and the Boolean algebra, possibly closed under quotient, generated by the languages of the form \(u^*\), where u is a word. We provide effective equational characterisations of these classes, i.e. one can decide using our descriptions whether a given regular language belongs or not to each of them.
The second author is supported by WCMCS.
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References
Almeida, J., Volkov, M.V.: Profinite identities for finite semigroups whose subgroups belong to a given pseudovariety. J. Algebra Appl. 2(2), 137–163 (2003)
Almeida, J., Weil, P.: Relatively free profinite monoids: an introduction and examples. In: Semigroups, Formal Languages and Groups (York, 1993), of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 466, pp. 73–117. Kluwer Acad. Publ., Dordrecht (1995)
Gehrke, M., Grigorieff, S., Pin, J.É.: Duality and equational theory of regular languages. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 246–257. Springer, Heidelberg (2008)
Honkala, J.: On slender languages. In: Paun, B., Rozenberg, G., Salomaa, A. (eds.)Current Trends in Theoretical Computer Science, pp. 708–716. World Scientific Publishing, River Edge (2001)
Pin, J.É.: Mathematical foundations of automata theory. http://www.liafa.jussieu.fr/~jep/PDF/MPRI/MPRI.pdf
Pin, J.É.: Profinite methods in automata theory. In: Albers, S., Marion, J.-Y. (eds.) 26th International Symposium on Theoretical Aspects of Computer Science (STACS 2009), pp. 31–50. Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany (2009)
Pin, J.É., Straubing, H., Thérien, D.: Some results on the generalized star-height problem. Inf. Comput. 101, 219–250 (1992)
Reilly, N.R., Zhang, S.: Decomposition of the lattice of pseudovarieties of finite semigroups induced by bands. Algebra Univers. 44(3–4), 217–239 (2000)
Reiterman, J.: The Birkhoff theorem for finite algebras. Algebra Univers. 14(1), 1–10 (1982)
Schützenberger, M.P.: On finite monoids having only trivial subgroups. Inf. Control 8, 190–194 (1965)
Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Language Theory, vol. 1, chap. 2, pp. 679–746. Springer, Heidelberg (1997)
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Daviaud, L., Paperman, C. (2015). Classes of Languages Generated by the Kleene Star of a Word. In: Italiano, G., Pighizzini, G., Sannella, D. (eds) Mathematical Foundations of Computer Science 2015. MFCS 2015. Lecture Notes in Computer Science(), vol 9234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48057-1_13
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DOI: https://doi.org/10.1007/978-3-662-48057-1_13
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