A generalization of Cobham's theorem

Theory of Computing Systems

Volumn 31, Issue 2, 1998, Pages 169-185

  Durand, F ^a  

^a AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SCIENCE; MATHEMATICAL TECHNIQUES;

COBHAM'S THEOREM; DOMINANT EIGENVALUES; FIXED POINTS; MORPHISMS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 0032379320     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s002240000084     Document Type: Article

References (21)

1. J. P. Allouche, q-regular sequences and other generalizations of q-automatic sequences, Proc. Latin '92, Lecture Notes in Computer Science, Vol. 583, Springer-Verlag, Berlin, 1992, pp. 15-23.
2. A. Bés. An extension of the Cobham-Semënov theorem, Preprint, University of Paris 6 (1996).
3. V. Bruyère, G. Hansel, C. Michaux, and R. Villemaire, Logic and p-recognizable sets of integers, Bull. Belgian Math. Soc.-Simon Stevin, 2 (1994), 191-238.
4. G. Christol, T. Kamae, M. Mendes-France, and G. Rauzy, Suites Algébriques et Substitutions, Bull. Soc. Math. France, 108 (1980), 401-419.
5. A. Cobham, On the base-dependence of sets of numbers recognizable by finite automata, Math. Systems Theory, 3 (1969), 186-192.
6. A. Cobham, Uniform tag sequences, Math. Systems Theory, 6 (1972), 164-192.
7. F. Durand, A characterization of substitutive sequences using return words, Discrete Math., to appear.
8. S. Fabre, Substitutions et indépendance des systèmes de numération, Thèse, Univerité d' Aix-Marseille 11 (1992).
9. S. Fabre, Une généralisation du Théorème de Cobham, Acta Arith., 67 (1994), 197-208.
10. S. Fabre, Substitutions et β-systèmes de numération, Theoret. Comput. Sci., 137 (1995), 219-236.
11. I. Fagnot, Cobham's theorem and automaticity in non-standard bases, Preprint, University of Paris 6 (1996).
12. F. R. Gantmacher, Theory of Matrices, Vol. 2, Chelsea, New York, 1959.
13. G. Hansel, A propos d'un théorème de Cobham, Actes de la fête des mots, D. Perrin Ed., GRECO de programmation, Rouen, 1982.
14. D. A. Lind, The entropies of topological markov shifts and a related class of algebraic integers, Ergodic Theory Dynamical Systems, 4 (1984), 283-300.
15. D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, Cambridge, 1995.
16. C. Michaux and R. Villemaire, Cobham's theorem seen through the Büchi theorem, Lecture Notes in Computer Science, Vol. 700, Springer-Verlag, Berlin, 1993, pp. 325-334.
17. C. Michaux and R. Villemaire, Presburger arithmetic and recognizability of natural numbers by automata: new proofs of Cobham's and Semenov's theorems, Ann. Pure Appl. Logic, 77 (1996), 251-277.
18. F. Mignosi and P. Séébold, If a DOL language is k-power free, then it is circular, Automata, Languages and Programming (Lund, 1993), Lecture Notes in Computer Science, Vol. 700, Springer-Verlag, Berlin, 1993, pp. 507-518.
19. B. Mossé, Puissances de mots et reconnaissabilité des points fixes d'une substitution, Theoret. Comput. Sci., 99 (1992), 327-334.
20. M. Queffélec, Substitution Dynamical Systems - Spectral Analysis, Lecture Notes in Mathematics, Vol. 1294, Springer-Verlag, Berlin, 1987.
21. A. L. Semenov, The Presburger nature of predicates that are regular in two number systems, Siberian Math. J., 18 (1977), 289-299.