J. Abdeljaoued and H. Lombardi, Méthodes matricielles : Introduction à la Complexité Algébrique, Mathématiques & applications, 2004.

B. Adamczewski and T. Rivoal, Irrationality measures for some automatic real numbers, Mathematical Proceedings of the Cambridge Philosophical Society, vol.392, issue.03, pp.659-678, 2009.
DOI : 10.2307/1988833
URL : https://hal.archives-ouvertes.fr/hal-00951118

A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms, 1974.

J. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Science, vol.98, issue.2, pp.163-197, 1992.
DOI : 10.1016/0304-3975(92)90001-V

J. Allouche and J. Shallit, The ubiquitous Prouhet-Thue-Morse sequence. Dans Sequences and their applications, Discrete Math. Theor. Comput. Sci, pp.1-16, 1998.

J. Allouche and J. Shallit, Automatic sequences
DOI : 10.1017/cbo9780511546563

G. Barat, V. Berthé, P. Liardet, and J. Thuswaldner, Dynamical directions in numeration. Annales de l'institut Fourier, pp.1987-2092, 2006.
URL : https://hal.archives-ouvertes.fr/lirmm-00130853

J. P. Bell and M. Coons, Transcendence tests for Mahler functions Récupéré le 6 mars, 2015.

J. L. Bentley, D. Haken, and J. B. Saxe, A general method for solving divide-and-conquer recurrences, ACM SIGACT News, vol.12, issue.3, pp.36-44, 1980.
DOI : 10.1145/1008861.1008865

J. Berstel and C. Reutenauer, Noncommutative Rational Series with Applications. Encyclopedia of Mathematics and its Applications, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00620617

J. Berstel and C. Reutenauer, Les séries rationnelles et leurs langages, 1984.

J. Berstel and C. Reutenauer, Rational series and their languages, EATCS Monographs on Theoretical Computer Science, vol.12, 1988.
DOI : 10.1007/978-3-642-73235-5
URL : https://hal.archives-ouvertes.fr/hal-00619791

P. Billingsley, Probability and measure Wiley Series in Probability and Mathematical Statistics : Probability and Mathematical Statistics, 1995.

D. Vincent, J. Blondel, . Cassaigne, M. Raphaël, and . Jungers, On the number of ?-power-free binary words for 2 < ? ? 7/3, Theoret. Comput. Sci, vol.410, pp.30-322823, 2009.

A. Bostan, F. Chyzak, M. Giusti, R. Lebreton, G. Lecerf et al., Algorithmes Efficaces en Calcul Formel. Récupéré le 6 mars 2016 de http, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01431717

J. Brillhart and L. Carlitz, Note on the Shapiro polynomials, Proc. Amer, pp.114-118, 1970.
DOI : 10.1090/S0002-9939-1970-0260955-6

J. Brillhart, P. Erd?s, and P. Morton, On sums of Rudin-Shapiro coefficients. II, Pacific Journal of Mathematics, vol.107, issue.1, pp.39-69, 1983.
DOI : 10.2140/pjm.1983.107.39

J. Brillhart and P. Morton, Über Summen von Rudin-Shapiroschen Koeffizienten, Illinois J. Math, vol.22, issue.1, pp.126-148, 1978.

J. Brillhart and P. Morton, A Case Study in Mathematical Research: The Golay-Rudin-Shapiro Sequence, The American Mathematical Monthly, vol.103, issue.10, pp.854-869, 1996.
DOI : 10.2307/2974610

J. Cassaigne, Counting overlap-free binary words, STACS 93, pp.216-225, 1993.
DOI : 10.1007/3-540-56503-5_24

H. Y. Louis, H. Chen, V. Hwang, and . Zacharovas, Distribution of the sum-of-digits function of random integers : a survey, Probababilty Surveys, vol.11, pp.177-236, 2014.

G. Christol, Ensembles presque periodiques k-reconnaissables, Theoretical Computer Science, vol.9, issue.1, pp.141-145, 1979.
DOI : 10.1016/0304-3975(79)90011-2

G. Christol, T. Kamae, M. M. France, and G. Rauzy, Suites alg??briques, automates et substitutions, Bulletin de la Soci&#233;t&#233; math&#233;matique de France, vol.79, issue.4, pp.401-419, 1980.
DOI : 10.24033/bsmf.1926
URL : http://archive.numdam.org/article/BSMF_1980__108__401_0.pdf

F. Chyzak, T. Dreyfus, P. Dumas, and M. Mezzaroba, Computing solutions of linear Mahler equations
URL : https://hal.archives-ouvertes.fr/hal-01418653

J. Coquet, A summation formula related to the binary digits, Inventiones Mathematicae, vol.32, issue.2, pp.107-115, 1983.
DOI : 10.1007/BF01393827

H. Thomas, C. E. Cormen, R. L. Leiserson, and . Rivest, Introduction to algorithms. The MIT Electrical Engineering and Computer Science Series, 1990.

I. Daubechies and J. C. Lagarias, Two-Scale Difference Equations. I. Existence and Global Regularity of Solutions, SIAM Journal on Mathematical Analysis, vol.22, issue.5, pp.1388-1410, 1991.
DOI : 10.1137/0522089

I. Daubechies and J. C. Lagarias, Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals, SIAM Journal on Mathematical Analysis, vol.23, issue.4, pp.1031-1079, 1992.
DOI : 10.1137/0523059

N. G. De-bruijn, On Mahler's partition problem, Indagationes Mathematicae, vol.10, pp.210-220, 1948.

J. W. Demmel, Applied Numerical Linear Algebra, Society for Industrial and Applied Mathematics, 1997.
DOI : 10.1137/1.9781611971446

L. David, . Donoho, P. Thomas, and . Yu, Deslariers-Dubuc : Ten years after, Spline Functions and the Theory of Wavelets CRM (Centre de Recherches Mathématiques) Proceedings & Lectures Notes, pp.355-369, 1999.

T. Dreyfus, C. Hardouin, and J. Roques, Hypertranscendance of solutions of Mahler equations, J. Eur. Math. Soc, 2015.

M. Drmota, J. Peter, and . Grabner, Analysis of digital functions and applications. Dans Combinatorics, automata and number theory, Encyclopedia Math. Appl, vol.135, pp.452-504, 2010.

M. Drmota, G. Larcher, and F. Pillichshammer, Precise distribution properties of the van der Corput sequence and related sequences, manuscripta mathematica, vol.21, issue.1, pp.11-41, 2005.
DOI : 10.1007/s00229-005-0577-y

S. Dubuc, Interpolation through an iterative scheme, Journal of Mathematical Analysis and Applications, vol.114, issue.1, pp.185-204, 1986.
DOI : 10.1016/0022-247X(86)90077-6

P. Dumas, Récurrences mahlériennes, suites automatiques, études asymptotiques, Thèse de doctorat, 1993.

P. Dumas, Joint spectral radius, dilation equations, and asymptotic behavior of radix-rational sequences, Linear Algebra and its Applications, vol.438, issue.5, pp.2107-2126, 2013.
DOI : 10.1016/j.laa.2012.10.013
URL : https://hal.archives-ouvertes.fr/hal-00780568

N. J. Fine, Binomial Coefficients Modulo a Prime, The American Mathematical Monthly, vol.54, issue.10, pp.589-592, 1947.
DOI : 10.2307/2304500

N. and P. Fogg, Substitutions in dynamics, arithmetics and combinatorics, volume 1794 de Lecture Notes in Mathematics, 2002.

J. E. Marcel and . Golay, Static multislit spectrometry and its application to the panoramic display of infrared spectra, Journal of the Optical Society of America, vol.41, issue.7, pp.468-472, 1951.

P. Henrici, Applied and computational complex analysis Special functions -Integral transforms -Asymptotics -Continued fractions

R. Jungers, The joint spectral radius, Lecture Notes in Control and Information Sciences Theory and applications, vol.385, 2009.
DOI : 10.1007/978-3-540-95980-9

T. Kisiekewski, Criteria for regularity of Mahler power series and Becker's conjecture, 2015. Récupéré le 6 mars 2016 de http

E. Donald and . Knuth, The art of computer programming Sorting and searching, Series in Computer Science and Information Processing, 1973.

B. Benoit, R. H. Mandelbrot, and . Riedi, Inverse measures, the inversion formula, and discontinuous multifractals, Adv. in Appl. Math, vol.18, issue.1, pp.50-58, 1997.

A. Charles, H. Micchelli, and . Prautzsch, Uniform refinement of curves. Linear Algebra and its Applications, pp.841-870, 1989.

D. J. Newman, On the number of binary digits in a multiple of three, Proc. Amer, pp.719-721, 1969.
DOI : 10.1090/S0002-9939-1969-0244149-8

S. Northshield, Stern's Diatomic Sequence 0,1,1,2,1,3,2,3,1,4,???, The American Mathematical Monthly, vol.117, issue.7, pp.581-598, 2010.
DOI : 10.4169/000298910x496714

O. Ore, Theory of Non-Commutative Polynomials, The Annals of Mathematics, vol.34, issue.3, pp.480-508, 1933.
DOI : 10.2307/1968173

J. Oudinet, Approches combinatoires pour le test statistique à grande échelle, Thèse de doctorat, 2010.

J. Oudinet, A. Denise, and M. Gaudel, A new dichotomic algorithm for the uniform random generation of words in regular languages. Dans Conference on random and exhaustive generation of combinatorial objects (GASCom), 2010.
URL : https://hal.archives-ouvertes.fr/inria-00542683

P. Franco, I. Preparata, and . Shamos, Computational geometry An introduction. Texts and Monographs in Computer Science, 1985.

H. William, S. A. Press, W. T. Teukolsky, B. P. Vetterling, and . Flannery, Numerical Recipes 3rd Edition : The Art of Scientific Computing, 2007.

M. R. , Y. Gao, and H. Lu, Numeration systems : a link between number theory and formal language theory Shinnosuke Seki et Sheng Yu (dir.) Developments in Language Theory, 14th International Conference, pp.33-53, 2010.

G. Rota and G. Strang, A note on the joint spectral radius, Proc. Ser. A 63 = Indag, pp.379-381, 1960.

W. Rudin, Some theorems on Fourier coefficients, Proceedings of the American Mathematical Society, vol.10, issue.6, pp.855-859, 1959.
DOI : 10.1090/S0002-9939-1959-0116184-5

B. Salvy, Conversation privée, 2013.

S. Harold and . Shapiro, Extremal problems for polynomials and power series, Thèse de maîtrise, Massachusets Institute of Technology, 1951.

G. Strang, Wavelets and Dilation Equations: A Brief Introduction, SIAM Review, vol.31, issue.4, pp.614-627, 1989.
DOI : 10.1137/1031128

J. Theys, Joint Spectral Radius : theory and applications, Thèse de doctorat, 2005.

C. Yap, A Real Elementary Approach to the Master Recurrence and Generalizations. Dans Theory and Applications of Models of Computation -8th Annual Conference, pp.14-26, 2011.