Abstract
In this paper we prove that it is decidable whether the set pow(L), which we get by taking all the powers of all the words in some regular language L, is regular or not. The problem was originally posed by Calbrix and Nivat in 1995. Partial solutions have been given by Cachat for unary languages and by Horváth et al. for various kinds of exponent sets for the powers and regular languages which have primitive roots satisfying certain properties. We show that the regular languages which have a regular power are the ones which are ’almost’ equal to their Kleene-closure.
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Anderson, T., Rampersad, N., Santean, N., Shallit, J.: Finite Automata, Palindromes, Powers, and Patterns. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 52–63. Springer, Heidelberg (2008)
Cachat, T.: The Power of One-Letter Rational Languages. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds.) DLT 2001. LNCS, vol. 2295, pp. 145–154. Springer, Heidelberg (2002)
Calbrix, H., Nivat, M.: Prefix and Period Languages of Rational omega-Languages. In: Dassow, J., Rozenberg, G., Salomaa, A. (eds.) Developments in Language Theory 1995, pp. 341–349. World Scientific, Singapore (1996)
Dömösi, P., Horváth, G., Ito, M.: A small hierarchy of languages consisting of non-primitive words. Publ. Math. Debrecen 64(3-4), 261–267 (2004)
Horváth, S., Leupold, P., Lischke, G.: Roots and Powers of Regular Languages. In: Ito, M., Toyama, M. (eds.) DLT 2002. LNCS, vol. 2450, pp. 220–230. Springer, Heidelberg (2003)
Lischke, G.: The root of a language and its complexity. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds.) DLT 2001. LNCS, vol. 2295, pp. 272–280. Springer, Heidelberg (2002)
Lyndon, R.C., Schützenberger, M.P.: On the equation a M = b N c P in a free group. Michigan Math. Journ. 9, 289–298 (1962)
Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM J. Res. Develop. 3, 114–125 (1959)
Shyr, H.J., Yu, S.S.: Non-primitive words in the language p + q + . Soochow J. Math. 20, 535–546 (1994)
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Fazekas, S.Z. (2009). Powers of Regular Languages. In: Diekert, V., Nowotka, D. (eds) Developments in Language Theory. DLT 2009. Lecture Notes in Computer Science, vol 5583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02737-6_17
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DOI: https://doi.org/10.1007/978-3-642-02737-6_17
Publisher Name: Springer, Berlin, Heidelberg
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