An analogue of Cobham's theorem for graph directed iterated function systems

Adamczewski, 2011, An analogue of Cobham's theorem for fractals, Trans. Amer. Math. Soc., 363, 4421, 10.1090/S0002-9947-2011-05357-2 Arnoux, 2001, Pisot substitutions and Rauzy fractals, Bull. Belg. Math. Soc. Simon Stevin, 8, 181, 10.36045/bbms/1102714169 Barnsley, 1985, Iterated function systems and the global construction of fractals, Proc. R. Soc. Lond. Ser. A, 399, 243, 10.1098/rspa.1985.0057 Berend, 1994, Computability by finite automata and Pisot bases, Math. Syst. Theory, 27, 275, 10.1007/BF01578846 Bertrand-Mathis, 1989, Comment écrire les nombres entiers dans une base qui n'est pas entière, Acta Math. Hungar., 54, 237, 10.1007/BF01952053 Boigelot, 2009, A generalization of Cobham's theorem to automata over real numbers, Theoret. Comput. Sci., 410, 1694, 10.1016/j.tcs.2008.12.051 Boigelot, 1997, An improved reachability analysis method for strongly linear hybrid systems, vol. 1254, 167 Boigelot, 1998, On the expressiveness of real and integer arithmetic automata (extended abstract), 152 Boigelot, 2001, On the use of weak automata for deciding linear arithmetic with integer and real variables, vol. 2083, 611 Boigelot, 2005, An effective decision procedure for linear arithmetic over the integers and reals, ACM Trans. Comput. Log., 6, 614, 10.1145/1071596.1071601 Boigelot, 2008, On the sets of real numbers recognized by finite automata in multiple bases, vol. 5126, 112 Boigelot, 2009, A generalization of Semenov's theorem to automata over real numbers, vol. 5663, 469 Boigelot, 2010, On the sets of real numbers recognized by finite automata in multiple bases, Log. Methods Comput. Sci., 6, 10.2168/LMCS-6(1:6)2010 Bruyère, 1994, Logic and p-recognizable sets of integers, Bull. Belg. Math. Soc. Simon Stevin, 1, 191, 10.36045/bbms/1103408547 Chan, 2014, A multi-dimensional analogue of Cobham's theorem for fractals, Proc. Amer. Math. Soc., 142, 449, 10.1090/S0002-9939-2013-11843-5 Cobham, 1969, On the base-dependence of sets of numbers recognizable by finite automata, Math. Syst. Theory, 3, 186, 10.1007/BF01746527 Daubechies, 2006, Robust and practical analog-to-digital conversion with exponential precision, IEEE Trans. Inform. Theory, 52, 3533, 10.1109/TIT.2006.878220 Daubechies, 2010, The golden ratio encoder, IEEE Trans. Inform. Theory, 56, 5097, 10.1109/TIT.2010.2059750 Durand, 2011, Cobham's theorem for substitutions, J. Eur. Math. Soc. (JEMS), 13, 1799 Edgar, 2008, Measure, Topology, and Fractal Geometry, 10.1007/978-0-387-74749-1 Elekes, 2010, Self-similar and self-affine sets: measure of the intersection of two copies, Ergodic Theory Dynam. Systems, 30, 399, 10.1017/S0143385709000121 Feng, 2009, On the structures of generating iterated function systems of Cantor sets, Adv. Math., 222, 1964, 10.1016/j.aim.2009.06.022 Ferrante, 1975, A decision procedure for the first order theory of real addition with order, SIAM J. Comput., 4, 69, 10.1137/0204006 Frougny, 1992, Representations of numbers and finite automata, Math. Syst. Theory, 25, 37, 10.1007/BF01368783 Frougny, 2010, Number representation and finite automata, vol. 135, 34 Hutchinson, 1981, Fractals and self-similarity, Indiana Univ. Math. J., 30, 713, 10.1512/iumj.1981.30.30055 Löding, 2001, Efficient minimization of deterministic weak ω-automata, Inform. Process. Lett., 79, 105, 10.1016/S0020-0190(00)00183-6 Lothaire, 2002, Algebraic Combinatorics on Words, vol. 90 Parry, 1960, On the β-expansions of real numbers, Acta Math. Acad. Sci. Hung., 11, 401, 10.1007/BF02020954 Pin, 2004 Pisot, 1946, Répartition (mod1) des puissances successives des nombres réels, Comment. Math. Helv., 19, 153, 10.1007/BF02565954 Rauzy, 1982, Nombres algébriques et substitutions, Bull. Soc. Math. France, 110, 147, 10.24033/bsmf.1957 Sirvent, 2002, Self-affine tiling via substitution dynamical systems and Rauzy fractals, Pacific J. Math., 206, 465, 10.2140/pjm.2002.206.465