  We revisit the problem of finding the conditions under which synchronous
probabilistic cellular automata indexed by the line $\mathbb{Z}$, or the
periodic line $\cyl{n}$, depending on 2 neighbours, admit as invariant
distribution the law of a space-indexed Markov chain. Our advances concerns PCA
defined on a finite alphabet, where most of existing results concern size 2
alphabet. A part of the paper is also devoted to the comparison of different
structures ($\mathbb{Z}$, $\cyl{n}$, and also some structures constituted with
two consecutive lines of the space time diagram) with respect to the property
to possess a Markovian invariant distribution.
