Abstract
Recently, Almeida, Margolis, Volkov and I have applied matrix representation theory [1] to give a simpler proof of results of Péladeau [4] and Weil [5] concerning marked products with counter. Eilenberg’s theorem characterizing languages recognized by p-groups [2] is a special case of these results. In these proceedings I will give a simple proof of Eilenberg’s Theorem based on representation theory that I came up with for a graduate course. The ideas are similar to those used in [1], which I presented during the conference.
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References
Almeida, J., Margolis, S.W., Steinberg, B., Volkov, M.V.: Representation theory of finite semigroups, semigroup radicals and formal language theory. Trans. Amer. Math. Soc. (to appear)
Eilenberg, S.: Automata, languages, and machines. Vol. B. Academic Press, New York (1976); Tilson, B.: Depth decomposition theorem, Complexity of semigroups and morphisms. In: Pure and Applied Mathematics, Vol. 59 (1976)
Lothaire, M.: Combinatorics on words. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1997)
Péladeau, P.: Sur le produit avec compteur modulo un nombre premier. RAIRO Inform. Théor. Appl. 26(6), 553–564 (1992)
Weil, P.: Closure of varieties of languages under products with counter. J. Comput. System Sci. 45(3), 316–339 (1992)
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Steinberg, B. (2008). Subsequence Counting, Matrix Representations and a Theorem of Eilenberg. In: Martín-Vide, C., Otto, F., Fernau, H. (eds) Language and Automata Theory and Applications. LATA 2008. Lecture Notes in Computer Science, vol 5196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88282-4_3
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DOI: https://doi.org/10.1007/978-3-540-88282-4_3
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