Connection between automatic sequences and endomorphisms of rooted trees via d-adic dynamics.

Authors

  • D.M. Savchuk Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620, USA
  • R. I. Grigorchuk Department of Mathematics, Texas A&M University, College Station, TX, 77843, USA

Keywords:

p-adic numbers, groups generated by automata, Mealy automata, Moore Automata, automatic sequences

Abstract

Connection between automatic sequences and endomorphisms of rooted trees via d-adic dynamics.

References

Elsayed Ahmed and Dmytro Savchuk, Endomorphisms of regular rooted trees induced by the action of polynomials on the ring Z.. of ..-adic integers, submitted, Preprint: arxiv:1711.06735, 2018.

Jean-Paul Allouche and Jeffrey Shallit, Automatic sequences, Cambridge University Press, Cambridge, 2003, Theory, applications, generalizations. MR 1997038

V. Anashin, Automata finiteness criterion in terms of van der Put series of automata functions, p-Adic Numbers Ultrametric Anal. Appl. 4 (2012), no. 2, 151–160. MR 2915627

V. S. Anashin, A. Yu. Khrennikov, and E. I. Yurova, Characterization of ergodic ..-adic dynamical systems in terms of the van der Put basis, Dokl. Akad. Nauk 438 (2011), no. 2, 151–153. MR 2857398

R. I. Grigorchuk, V. V. Nekrashevich, and V. I. Sushchanski.., Automata, dynamical systems, and groups, Tr. Mat. Inst. Steklova 231 (2000), no. Din. Sist., Avtom. i Beskon. Gruppy, 134–214. MR MR1841755 (2002m:37016)

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