Profinite automata

نویسندگان

  • Eric Rowland
  • Reem Yassawi
چکیده

Many sequences of p-adic integers project modulo p to p-automatic sequences for every α ≥ 0. Examples include algebraic sequences of integers, which satisfy this property for every prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. For such a sequence, we construct a profinite automaton that projects modulo p to the automaton generating the projected sequence. In general, the profinite automaton has infinitely many states. Additionally, we consider the closure of the orbit, under the shift map, of the p-adic integer sequence, defining a shift dynamical system. We describe how this shift is a letter-to-letter coding of a shift generated by a constantlength substitution defined on an uncountable alphabet, and we establish some dynamical properties of these shifts.

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عنوان ژورنال:
  • CoRR

دوره abs/1403.7659  شماره 

صفحات  -

تاریخ انتشار 2014