Probabilistic functions and statistical equivalence of binary shift registers with random Markov input

We consider a binary non-autonomous shift register with a sequence of random variables connected into a simple homogeneous stationary Markov chain at the input. The expression is obtained for the probability function in the output sequence in the form of a fractional rational function, the arguments of which are the transition probabilities of the Markov chain. An equivalence relation arising in the case of the identical equality of the probability functions of the registers is described. The results known earlier for the case when the input sequence is a sequence of independent random variables are generalized. © 2020 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org)