Suites algébriques, automates et substitutions
Bulletin de la Société Mathématique de France, Tome 108 (1980), pp. 401-419. 
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     title = {Suites alg\'ebriques, automates et substitutions},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {401--419},
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     zbl = {0472.10035},
     language = {fr},
     url = {https://www.numdam.org/articles/10.24033/bsmf.1926/}
}
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Christol, G.; Kamae, T.; Mendès France, Michel; Rauzy, Gérard. Suites algébriques, automates et substitutions. Bulletin de la Société Mathématique de France, Tome 108 (1980), pp. 401-419. doi : 10.24033/bsmf.1926. https://www.numdam.org/articles/10.24033/bsmf.1926/

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  • Barbé, A.; von Haeseler, F. Symmetries of decimation invariant sequences and digit sets, Theoretical Computer Science, Volume 289 (2002) no. 1, p. 105 | DOI:10.1016/s0304-3975(01)00193-1
  • Carpi, Arturo; Maggi, Cristiano On synchronized sequences and their separators, RAIRO - Theoretical Informatics and Applications, Volume 35 (2001) no. 6, p. 513 | DOI:10.1051/ita:2001129
  • Barbé, A.; Skordev, G. Decimation-invariant sequences and their automaticity, Theoretical Computer Science, Volume 259 (2001) no. 1-2, p. 379 | DOI:10.1016/s0304-3975(00)00021-9
  • Vuillemin, Jean Finite Digital Synchronous Circuits Are Characterized by 2-Algebraic Truth Tables, Advances in Computing Science — ASIAN 2000, Volume 1961 (2000), p. 1 | DOI:10.1007/3-540-44464-5_1
  • Fresnel, Jean; Koskas, Michel; de Mathan, Bernard Automata and Transcendence in Positive Characteristic, Journal of Number Theory, Volume 80 (2000) no. 1, p. 1 | DOI:10.1006/jnth.1999.2444
  • Anderson, G.W. An Elementary Approach to L-Functions modp, Journal of Number Theory, Volume 80 (2000) no. 2, p. 291 | DOI:10.1006/jnth.1999.2452
  • Allouche, Jean-Paul Algebraic and Analytic Randomness, Noise, Oscillators and Algebraic Randomness, Volume 550 (2000), p. 345 | DOI:10.1007/3-540-45463-2_17
  • Karamanos, K. From Symbolic Dynamics to a Digital Approach: Chaos and Transcendence, Noise, Oscillators and Algebraic Randomness, Volume 550 (2000), p. 357 | DOI:10.1007/3-540-45463-2_18
  • Lameche, Khira Inverse for the shuffle for algebraic series, Applied Mathematics and Computation, Volume 98 (1999) no. 1, p. 1 | DOI:10.1016/s0096-3003(97)10059-5
  • Allouche, J.-P. Cellular Automata, Finite Automata, and Number Theory, Cellular Automata (1999), p. 321 | DOI:10.1007/978-94-015-9153-9_13
  • Yao, Jia-yan Opacités des automates finis, Discrete Mathematics, Volume 202 (1999) no. 1-3, p. 279 | DOI:10.1016/s0012-365x(98)00361-6
  • Shallit, Jeffrey Number Theory and Formal Languages, Emerging Applications of Number Theory, Volume 109 (1999), p. 547 | DOI:10.1007/978-1-4612-1544-8_22
  • BARBÉ, ANDRÉ; PEITGEN, HEINZ-OTTO; SKORDEV, GENCHO AUTOMATICITY OF COARSE-GRAINING INVARIANT ORBITS OF ONE-DIMENSIONAL LINEAR CELLULAR AUTOMATA, International Journal of Bifurcation and Chaos, Volume 09 (1999) no. 01, p. 67 | DOI:10.1142/s0218127499000043
  • Allouche, Jean-Paul; Thakur, Dinesh Automata and transcendence of the Tate period in finite characteristic, Proceedings of the American Mathematical Society, Volume 127 (1999) no. 5, p. 1309 | DOI:10.1090/s0002-9939-99-04650-x
  • Allouche, Jean-Paul; Shallit, Jeffrey The Ubiquitous Prouhet-Thue-Morse Sequence, Sequences and their Applications (1999), p. 1 | DOI:10.1007/978-1-4471-0551-0_1
  • Barbé, André Multiscale Coarse-graining Invariant Sequences, Sequences and their Applications (1999), p. 146 | DOI:10.1007/978-1-4471-0551-0_9
  • Von Haeseler, Fritz; Jürgensen, Wibke Automaticity of Solutions of Mahler Equations, Sequences and their Applications (1999), p. 228 | DOI:10.1007/978-1-4471-0551-0_16
  • Niederreiter, Harald Some Computable Complexity Measures for Binary Sequences, Sequences and their Applications (1999), p. 67 | DOI:10.1007/978-1-4471-0551-0_5
  • Allouche, J.-P. Transcendence of formal power series with rational coefficients, Theoretical Computer Science, Volume 218 (1999) no. 1, p. 143 | DOI:10.1016/s0304-3975(98)00256-4
  • Leblanc, B.; Lutton, E.; Allouche, J. -P. Inverse problems for finite automata: A solution based on genetic algorithms, Artificial Evolution, Volume 1363 (1998), p. 157 | DOI:10.1007/bfb0026598
  • Cadic, Christophe Modules de Drinfeld formels et algébricité, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, Volume 327 (1998) no. 4, p. 335 | DOI:10.1016/s0764-4442(99)80043-3
  • Durand, Fabien A characterization of substitutive sequences using return words, Discrete Mathematics, Volume 179 (1998) no. 1-3, p. 89 | DOI:10.1016/s0012-365x(97)00029-0
  • Sharif, Habib E-Algebraic Functions over Fields of Positive Characteristic—An Analogue of Differentially Algebraic Functions, Journal of Algebra, Volume 207 (1998) no. 2, p. 355 | DOI:10.1006/jabr.1998.7440
  • Queffélec, M. Transcendance des fractions continues de Thue–Morse, Journal of Number Theory, Volume 73 (1998) no. 2, p. 201 | DOI:10.1006/jnth.1998.2305
  • Bercoff, Christiane Uniform tag systems for paperfolding sequences, Discrete Applied Mathematics, Volume 77 (1997) no. 2, p. 119 | DOI:10.1016/s0166-218x(97)84103-0
  • Mendès France, Michel; Yao, Jia-yan Transcendence and the Carlitz–Goss Gamma Function, Journal of Number Theory, Volume 63 (1997) no. 2, p. 396 | DOI:10.1006/jnth.1997.2104
  • Garel, E. Séparateurs dans les mots infinis engendrés par morphismes, Theoretical Computer Science, Volume 180 (1997) no. 1-2, p. 81 | DOI:10.1016/s0304-3975(97)83808-x
  • Bruyère, Véronique; Hansel, Georges Bertrand numeration systems and recognizability, Theoretical Computer Science, Volume 181 (1997) no. 1, p. 17 | DOI:10.1016/s0304-3975(96)00260-5
  • Honkala, Juha On Lindenmayerian algebraic sequences, Theoretical Computer Science, Volume 183 (1997) no. 1, p. 143 | DOI:10.1016/s0304-3975(96)00314-3
  • Černý, Anton On sequences resulting from iteration of modified quadratic and palindromic mappings, Theoretical Computer Science, Volume 188 (1997) no. 1-2, p. 161 | DOI:10.1016/s0304-3975(96)00294-0
  • Allouche, J.-P; von Haeseler, F; Peitgen, H.-O; Petersen, A; Skordev, G Automaticity of double sequences generated by one-dimensional linear cellular automata, Theoretical Computer Science, Volume 188 (1997) no. 1-2, p. 195 | DOI:10.1016/s0304-3975(96)00298-8
  • Allouche, J. P.; Cateland, E.; Gilbert, W. J.; Peitgen, H. O.; Shallit, J. O.; Skordev, G. Automatic maps in exotic numeration systems, Theory of Computing Systems, Volume 30 (1997) no. 3, p. 285 | DOI:10.1007/bf02679463
  • Razafy Andriamampianina, D. Suites de toeplitz,p-pliage, suites automatiques et polynomes, Acta Mathematica Hungarica, Volume 73 (1996) no. 3, p. 179 | DOI:10.1007/bf02181049
  • Allouche, J.-P; von Haeseler, F; Peitgen, H.-O; Skordev, G Linear cellular automata, finite automata and Pascal's triangle, Discrete Applied Mathematics, Volume 66 (1996) no. 1, p. 1 | DOI:10.1016/0166-218x(94)00132-w
  • Tapsoba, Théodore Special factors of automatic sequences, Journal of Pure and Applied Algebra, Volume 108 (1996) no. 3, p. 301 | DOI:10.1016/0022-4049(95)00043-7
  • Lange, Ehler Substitutions for linear shift register sequences and the factorization algorithms of Berlekamp and Niederreiter, Linear Algebra and its Applications, Volume 249 (1996) no. 1-3, p. 217 | DOI:10.1016/0024-3795(95)00358-4
  • Bruyère, Véronique; Hansel, Georges Recognizable sets of numbers in nonstandard bases, LATIN '95: Theoretical Informatics, Volume 911 (1995), p. 167 | DOI:10.1007/3-540-59175-3_87
  • Tapsoba, T. Minimum complexity of automatic non sturmian sequences, RAIRO - Theoretical Informatics and Applications, Volume 29 (1995) no. 4, p. 285 | DOI:10.1051/ita/1995290402851
  • Garel, Emmanuelle On the separators on an infinite word generated by a morphism, STACS 95, Volume 900 (1995), p. 119 | DOI:10.1007/3-540-59042-0_67
  • Bercoff, Christiane A family of tag systems for paperfolding sequences, STACS 95, Volume 900 (1995), p. 303 | DOI:10.1007/3-540-59042-0_82
  • Denis, Laurent Méthodes fonctionnelles pour la transcendance en caractéristique finie, Bulletin of the Australian Mathematical Society, Volume 50 (1994) no. 2, p. 273 | DOI:10.1017/s0004972700013733
  • Dekking, F.M. Iteration of maps by an automaton, Discrete Mathematics, Volume 126 (1994) no. 1-3, p. 81 | DOI:10.1016/0012-365x(94)90254-2
  • Blanchard, F.; Fabre, S. Quelques procédés engendrant des suites infinies, Theoretical Computer Science, Volume 123 (1994) no. 1, p. 55 | DOI:10.1016/0304-3975(94)90068-x
  • Allouche, Jean-Paul; Bousquet-Mélou, Mireille Canonical positions for the factors in paperfolding sequences, Theoretical Computer Science, Volume 129 (1994) no. 2, p. 263 | DOI:10.1016/0304-3975(94)90028-0
  • Becker, Paul-Georg Automatische Folgen und Transzendenz in positiver Charakteristik, Archiv der Mathematik, Volume 61 (1993) no. 1, p. 68 | DOI:10.1007/bf01258057
  • Dumas, Ph. Algebraic aspects of B-regular series, Automata, Languages and Programming, Volume 700 (1993), p. 457 | DOI:10.1007/3-540-56939-1_94
  • van der Poorten, A. J. Power series representing algebraic functions, Séminaire de Théorie des Nombres, Paris, 1990–91 (1993), p. 241 | DOI:10.1007/978-1-4757-4271-8_11
  • Lehr, S. Sums and rational multiples of q-automatic sequences are q-automatic, Theoretical Computer Science, Volume 108 (1993) no. 2, p. 385 | DOI:10.1016/0304-3975(93)90202-5
  • Litow, B.; Dumas, Ph. Additive cellular automata and algebraic series, Theoretical Computer Science, Volume 119 (1993) no. 2, p. 345 | DOI:10.1016/0304-3975(93)90165-p
  • Allouche, Jean-Paul The number of factors in a paperfolding sequence, Bulletin of the Australian Mathematical Society, Volume 46 (1992) no. 1, p. 23 | DOI:10.1017/s0004972700011655
  • Axel, F; Allouche, J -P; Wen, Zhi-Ying On certain properties of high-resolution X-ray diffraction spectra of finite-size generalized Rudin-Shapiro multilayer heterostructures, Journal of Physics: Condensed Matter, Volume 4 (1992) no. 45, p. 8713 | DOI:10.1088/0953-8984/4/45/007
  • Allouche, Jean-Paul q-Regular sequences and other generalizations of q-automatic sequences, LATIN '92, Volume 583 (1992), p. 15 | DOI:10.1007/bfb0023813
  • Allouche, Jean-Paul; Morton, Patrick; Shallit, Jeffrey Pattern spectra, substring enumeration, and automatic sequences, Theoretical Computer Science, Volume 94 (1992) no. 2, p. 161 | DOI:10.1016/0304-3975(92)90032-b
  • Wen, Zhi-Xiong; Wen, Zhi-Ying Some studies on the (p, q)-type sequences, Theoretical Computer Science, Volume 94 (1992) no. 2, p. 373 | DOI:10.1016/0304-3975(92)90045-h
  • Allouche, Jean-Paul; Shallit, Jeffrey The ring of k-regular sequences, Theoretical Computer Science, Volume 98 (1992) no. 2, p. 163 | DOI:10.1016/0304-3975(92)90001-v
  • Dumont, J.M.; Thomas, A. Digital sum problems and substitutions on a finite alphabet, Journal of Number Theory, Volume 39 (1991) no. 3, p. 351 | DOI:10.1016/0022-314x(91)90054-f
  • Morton, Patrick; Mourant, W. J. Digit patterns and transcendental numbers, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 51 (1991) no. 2, p. 216 | DOI:10.1017/s1446788700034200
  • van der Poorten, A. J. Kurt Mahler, 1903–1988, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 51 (1991) no. 3, p. 343 | DOI:10.1017/s1446788700034558
  • Kolář, M.; Ali, M. K.; Nori, Franco Generalized Thue-Morse chains and their physical properties, Physical Review B, Volume 43 (1991) no. 1, p. 1034 | DOI:10.1103/physrevb.43.1034
  • Axel, Françoise; Terauchi, Hikaru High-resolution x-ray-diffraction spectra of Thue-Morse GaAs-AlAs heterostructures: Towards a novel description of disorder, Physical Review Letters, Volume 66 (1991) no. 17, p. 2223 | DOI:10.1103/physrevlett.66.2223
  • Séébold, Patrice Fibonacci morphisms and Sturmian words, Theoretical Computer Science, Volume 88 (1991) no. 2, p. 365 | DOI:10.1016/0304-3975(91)90383-d
  • Allouche, J. -P.; Flajolet, P.; France, M. Mendes Algebraically independent formal power series: A language theory interpretation, Analytic Number Theory, Volume 1434 (1990), p. 11 | DOI:10.1007/bfb0097121
  • Harase, Takashi Algebraic dependence of formal power series, Analytic Number Theory, Volume 1434 (1990), p. 133 | DOI:10.1007/bfb0097129
  • Allouche, Jean-Paul; Shallit, Jeffrey Sums of digits and the Hurwitz zeta function, Analytic Number Theory, Volume 1434 (1990), p. 19 | DOI:10.1007/bfb0097122
  • PERRIN, Dominique Finite Automata, Formal Models and Semantics (1990), p. 1 | DOI:10.1016/b978-0-444-88074-1.50006-8
  • Allouche, J.-P. Finite Automata in 1-D and 2-D Physics, Number Theory and Physics, Volume 47 (1990), p. 177 | DOI:10.1007/978-3-642-75405-0_18
  • Dumont, J. M. Summation Formulae for Substitutions on a Finite Alphabet, Number Theory and Physics, Volume 47 (1990), p. 185 | DOI:10.1007/978-3-642-75405-0_19
  • Allouche, J.-P.; Dress, F. Tours de Hanoï et automates, RAIRO - Theoretical Informatics and Applications, Volume 24 (1990) no. 1, p. 1 | DOI:10.1051/ita/1990240100011
  • Allouche, Jean-Paul; Shallit, Jeffrey The ring of k-regular sequences, STACS 90, Volume 415 (1990), p. 12 | DOI:10.1007/3-540-52282-4_28
  • Shallit, Jeffrey; Stolfi, Jorge Two methods for generating fractals, Computers Graphics, Volume 13 (1989) no. 2, p. 185 | DOI:10.1016/0097-8493(89)90060-5
  • Séébold, Patrice About a family of binary morphisms which stationary words are Sturmian, Fundamentals of Computation Theory, Volume 380 (1989), p. 384 | DOI:10.1007/3-540-51498-8_37
  • Loxton, J. H. Spectral Studies of Automata, Irregularities of Partitions (1989), p. 115 | DOI:10.1007/978-3-642-61324-1_10
  • Harase, Takashi Algebraic elements in formal power series rings II, Israel Journal of Mathematics, Volume 67 (1989) no. 1, p. 62 | DOI:10.1007/bf02764899
  • France, Michel Mendès; Shallit, J.O Wire bending, Journal of Combinatorial Theory, Series A, Volume 50 (1989) no. 1, p. 1 | DOI:10.1016/0097-3165(89)90002-2
  • Axel, Fran�oise; Peyri�re, Jacques Spectrum and extended states in a harmonic chain with controlled disorder: Effects of the Thue-Morse symmetry, Journal of Statistical Physics, Volume 57 (1989) no. 5-6, p. 1013 | DOI:10.1007/bf01020046
  • Tamura, S.; Nori, Franco Transmission and frequency spectra of acoustic phonons in Thue-Morse superlattices, Physical Review B, Volume 40 (1989) no. 14, p. 9790 | DOI:10.1103/physrevb.40.9790
  • Bleuzen-Guernalec, Noëlle; Blanc, Georges Production en temps réel et complexité de structure de suites infinies, RAIRO - Theoretical Informatics and Applications, Volume 23 (1989) no. 2, p. 195 | DOI:10.1051/ita/1989230201951
  • Allouche, J.-P.; Betrema, J.; Shallit, J. O. Sur des points fixes de morphismes d'un monoïde libre, RAIRO - Theoretical Informatics and Applications, Volume 23 (1989) no. 3, p. 235 | DOI:10.1051/ita/1989230302351
  • Shallit, Jeffrey A generalization of automatic sequences, STACS 89, Volume 349 (1989), p. 156 | DOI:10.1007/bfb0028981
  • Allouche, Jean-Paul On a sequence of rational functions, Theoretical Computer Science, Volume 65 (1989) no. 2, p. 123 | DOI:10.1016/0304-3975(89)90037-6
  • Dumont, Jean-Marie; Thomas, Alain Systemes de numeration et fonctions fractales relatifs aux substitutions, Theoretical Computer Science, Volume 65 (1989) no. 2, p. 153 | DOI:10.1016/0304-3975(89)90041-8
  • Harase, Takashi Algebraic elements in formal power series rings, Israel Journal of Mathematics, Volume 63 (1988) no. 3, p. 281 | DOI:10.1007/bf02778035
  • Mauduit, Christian Sur l'ensemble normal des substitutions de longueur quelconque, Journal of Number Theory, Volume 29 (1988) no. 3, p. 235 | DOI:10.1016/0022-314x(88)90103-5
  • Lemańczyk, M. Weakly isomorphic transformations that are not isomorphic, Probability Theory and Related Fields, Volume 78 (1988) no. 4, p. 491 | DOI:10.1007/bf00353873
  • Allouche, Jean-Paul; Rande, Bernard; Thimonier, Loÿs Fonctions Generatrices Transcendantes a Coefficients Engendres par Automates, STACS 88, Volume 294 (1988), p. 170 | DOI:10.1007/bfb0035843
  • Shallit, Jeffrey A generalization of automatic sequences, Theoretical Computer Science, Volume 61 (1988) no. 1, p. 1 | DOI:10.1016/0304-3975(88)90103-x
  • Denef, J; Lipshitz, L Algebraic power series and diagonals, Journal of Number Theory, Volume 26 (1987) no. 1, p. 46 | DOI:10.1016/0022-314x(87)90095-3
  • Allouche, Jean-Paul The Ising Model And The Rudin-Shapiro Sequence, Disordered Systems and Biological Organization (1986), p. 59 | DOI:10.1007/978-3-642-82657-3_6
  • Grassberger, Peter Toward a quantitative theory of self-generated complexity, International Journal of Theoretical Physics, Volume 25 (1986) no. 9, p. 907 | DOI:10.1007/bf00668821
  • Allouche, Jean-Paul; France, Michel Mendes Quasicrystal Ising chain and automata theory, Journal of Statistical Physics, Volume 42 (1986) no. 5-6, p. 809 | DOI:10.1007/bf01010446
  • Séébold, Patrice Complément à l'étude des suites de Thue-Morse généralisées, RAIRO - Theoretical Informatics and Applications, Volume 20 (1986) no. 2, p. 157 | DOI:10.1051/ita/1986200201571
  • Mauduit, Christian Morphismes unispectraux, Theoretical Computer Science, Volume 46 (1986), p. 1 | DOI:10.1016/0304-3975(86)90018-6
  • Séébold, Patrice Generalized thue-morse sequences, Fundamentals of Computation Theory, Volume 199 (1985), p. 402 | DOI:10.1007/bfb0028824
  • Allouche, Jean-Paul; France, Michel Mendès On an extremal property of the Rudin‐Shapiro sequence, Mathematika, Volume 32 (1985) no. 1, p. 33 | DOI:10.1112/s0025579300010822
  • Černý, Anton On a class of infinite words with bounded repetitions, RAIRO. Informatique théorique, Volume 19 (1985) no. 4, p. 337 | DOI:10.1051/ita/1985190403371
  • Černý, A. On generalized words of Thue-Morse, Mathematical Foundations of Computer Science 1984, Volume 176 (1984), p. 232 | DOI:10.1007/bfb0030303
  • Berstel, Jean Some recent results on squarefree words, STACS 84, Volume 166 (1984), p. 14 | DOI:10.1007/3-540-12920-0_2
  • France, M. Mendès; van der Poorten, A. J.; Dekking, F. M. Folds!°, The Mathematical Intelligencer, Volume 4 (1982) no. 3, p. 130 | DOI:10.1007/bf03024244
  • Dekking, Michel; France, Michel Mendès; van der Poorten, Alf Folds, The Mathematical Intelligencer, Volume 4 (1982) no. 4, p. 173 | DOI:10.1007/bf03023552

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