Abstract
We present here new hierarchies of literal varieties of languages. Each language under consideration is a disjoint union of a certain collection of “basic” languages described here. Our classes of languages correspond to certain literal varieties of homomorphisms from free monoids onto nilpotent groups of class ≤ 2.
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References
Almeida, J.: Finite Semigroups and Universal Algebra. World Scientific, Singapore (1994)
Baldwin, J., Berman, J.: Varieties and finite closure conditions. Colloq. Math. 35, 15–20 (1976)
Carton, O., Pin, J.-E., Soler-Escrivà, X.: Languages recognized by finite supersoluble groups (submitted)
Eilenberg, S.: Automata, Languages and Machines, vol. A,B. Academic Press, New York (1974-1976)
Ésik, Z.: Extended temporal logic on finite words and wreath product of monoids with distinguished generators. In: Ito, M., Toyama, M. (eds.) DLT 2002. LNCS, vol. 2450, pp. 43–58. Springer, Heidelberg (2003)
Ésik, Z., Ito, M.: Temporal logic with cyclic counting and the degree of aperiodicity of finite automata. Acta Cybernetica 16, 1–28 (2003); a preprint BRICS 2001
Ésik, Z., Larsen, K.G.: Regular languages defined by Lindström quantifiers. Theoretical Informatics and Applications 37, 197–242 (2003); preprint BRICS 2002
Kunc, M.: Equational description of pseudovarieties of homomorphisms. Theoretical Informatics and Applications 37, 243–254 (2003)
Pin, J.-E.: Syntactic semigroups. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, ch. 10. Springer, Heidelberg (1997)
Pin, J.-E., Straubing, H.: Some results on C-varieties. Theoretical Informatics and Applications 39, 239–262 (2005)
Polák, L.: On varieties, generalized varieties and pseudovarieties of homomorphisms. In: Contributions to General Algebra, vol. 16, pp. 173–187. Verlag Johannes Heyn, Klagenfurt (2005)
Polák, L.: On varieties and pseudovarieties of homomorphisms onto abelian groups. In: Proc. International Conference on Semigroups and Languages, Lisboa 2005, pp. 255–264. World Scientific Publishing, Singapore (2007)
Straubing, H.: On logical descriptions of regular languages. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 528–538. Springer, Heidelberg (2002)
Thérien, D.: Languages of Nilpotent and Solvable Groups. In: Maurer, H.A. (ed.) ICALP 1979. LNCS, vol. 71, pp. 616–632. Springer, Heidelberg (1979)
Thérien, D.: Subwords counting and nilpotent groups. In: Cummings, L. (ed.) Combinatorics on Words, Progress and Perspectives, pp. 293–306. Academic Press, London (1983)
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Klíma, O., Polák, L. (2008). Literal Varieties of Languages Induced by Homomorphisms onto Nilpotent Groups. 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_28
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DOI: https://doi.org/10.1007/978-3-540-88282-4_28
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