Let X(n), n≥0, be a (homogeneous) Markov chain with a finite state space S={1,2,…,m}. Let S be the union of disjoint sets S1, S2,…,Sk which form a partition of S. Define Y(n)=i if and only if X(n)∈Si for i=1,2,…,k. Is the collapsed chain Y(n) Markov? This problem was considered by...