Abstract
There are several characterizations of sets of integers recognizable by automata, when they are written in p-ary representations, p≥2. We prove that most of them can be adapted to sets of integers written in nonstandard numeration systems, like Fibonacci numeration system.
This work was partially supported by ESPRIT-BRA Working Group 6317 ASMICS and Cooperation Project C.G.R.I.-C.N.R.S. Théorie des Automates et Applications.
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References
J.-P. Allouche, q-regular sequences and other generalizations of q-automatic sequences, Proc. Latin'92, Lecture Notes in Comput. Sci. 583 (1992) 15–23.
A. Bertrand-Mathis, Comment écrire les nombres entiers dans une base qui n'est pas entière, Acta Math. Acad. Sci. Hungar. 54 (1989) 237–241.
A. Bertrand-Mathis, Développement en base θ, répartition modulo un de la suite (xθ n)n≥0, langages codés et θ-shift, Bull. Soc. Math. France 114 (1986) 271–323.
V. Bruyère, G. Hansel, C. Michaux, R. Villemaire, Logic and p-recognizable sets of integers, Bull. Belg. Math. Soc. 1 (1994) 191–238.
J.R. Büchi, Weak second-order arithmetic and finite automata, Z. Math. Logik Grundlag. Math. 6 (1960) 66–92.
G. Christol, T. Kamae, M. Mendès France, G. Rauzy, Suites algébriques, automates et substitutions, Bull. Soc. Math. France 108 (1980) 401–419.
A. Cobham, On the base-dependence of sets of numbers recognizable by finite automata, Math. Systems Theory 3 (1969) 186–192.
A. Cobham, Uniform tag systems, Math. Systems Theory 6 (1972) 164–192.
S. Eilenberg, Automata, Languages and Machines, Vol. A, Academic Press, New York (1974).
S. Fabre, Substitutions et indépendence des systèmes de numération, Thèse, Université Aix-Marseille II (1992).
A.S. Fraenkel, Systems of numeration, Amer. Math. Monthly 92 (1985) 105–114.
C. Frougny, B. Solomyak, On representations of integers in linear numeration systems, preprint, submitted (1994) 18 pages.
B.R. Hodgson, Décidabilité par automate fini, Ann. Sci. Math. Québec 7 (1983) 39–57.
W. Parry, On the β-expansions of real numbers, Acta Math. Acad. Sci. Hungar. 11 (1960) 401–416.
D. Perrin, Finite automata, in: Handbook of Theoretical Computer Science, vol. B, J. Van Leeuwen, Ed., Elsevier (1990) 2–57.
J. Shallit, A generalization of automatic sequences, Theoret. Comput. Sci. 61 (1988) 1–16.
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© 1995 Springer-Verlag Berlin Heidelberg
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Bruyère, V., Hansel, G. (1995). Recognizable sets of numbers in nonstandard bases. In: Baeza-Yates, R., Goles, E., Poblete, P.V. (eds) LATIN '95: Theoretical Informatics. LATIN 1995. Lecture Notes in Computer Science, vol 911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59175-3_87
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DOI: https://doi.org/10.1007/3-540-59175-3_87
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