On the trace subshifts of fractional multiplication automata

: Kopra Johan

: 2021

Theoretical Computer Science

: THEORETICAL COMPUTER SCIENCE

: THEOR COMPUT SCI

: 851

: 92

: 110

: 19

: 0304-3975

: 1879-2294

DOI: https://doi.org/10.1016/j.tcs.2020.11.010

: https://research.utu.fi/converis/portal/detail/Publication/51286958

We address the dynamics of the cellular automaton (CA) that multiplies by p/q in base pq (for coprime p > q > 1) by studying its trace subshift. We present a conjugacy of the trace to a previously studied base-p/q numeration system. We also show that the trace subshift is not synchronizing and in particular not sofic. As a byproduct we compute its complexity function and we conclude by presenting an example of a sofic shift with the same complexity function.

Trace of Fractional CA.pdf