Abstract
A rational relation is a rational subset of the direct product of two free monoids: R ⊆ A*× B*. Consider R as a function of A* into the family of subsets of B* by posing for all u ∈ A*, R (u) = {v ∈ B* | (u,v) ∈ R}. Assume R (u) is a finite set for all u ∈ A*. We study how the cardinality of R (u) behaves as the length of u tends to infinity and we show that there exists an infinite hierachy of growth functions.
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References
Berstel, J.: Transductions and context-free languages. B. G. Teubner (1979)
Bertoni, A., Choffrut, C., Goldwurm, M., Lonati, V.: On the number of occurrences of a symbol in words of regular languages. Theoret. Comput. Sci. 302(1-3), 431–456 (2003)
Eilenberg, S.: Automata, Languages and Machines, vol. A. Academic Press, London (1974)
Henrici, P.: Elements of numerical analysis. John Wiley, Chichester (1964)
Sakarovitch, J.: Eléments de théorie des automates. Vuibert Informatique (2003)
Salomaa, A., Soittola, M.: Automata-Theoretic Aspects of Formal Power Series. Texts and Monographs in Compuer Science. Springer, Heidelberg (1978)
Schützenberger, M.-P.: Finite counting automata. Information and Control 5, 91–107 (1962)
Schützenberger, M.-P.: Sur les relations rationnelles fonctionnelles entre monoïdes libres. Theoret. Comput. Sci. 9, 243–259 (1976)
Weber, A.: On the valuedness of finite transducers. Acta Informatica 27, 749–780 (1990)
Weber, A., Seidl, H.: On the degree of ambiguity of finite automata. Theoret. Comput. Sci. 88, 325–349 (1991)
Wich, K.: Sublinear ambiguity. In: Nielsen, M., Rovan, B. (eds.) MFCS 2000. LNCS, vol. 1893, pp. 690–698. Springer, Heidelberg (2000)
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Choffrut, C. (2004). Rational Relations as Rational Series. In: Karhumäki, J., Maurer, H., Păun, G., Rozenberg, G. (eds) Theory Is Forever. Lecture Notes in Computer Science, vol 3113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27812-2_3
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DOI: https://doi.org/10.1007/978-3-540-27812-2_3
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