We present an O(m \log n)-time minimization algorithm for almost of finite-type automata, where n is the number of states of the automaton and m its number of edges. (This is joint work with Maxime Crochemore). We then give a linear time construction of a constrained channel with periodic unconstrained positions from a finite type channel defined by forbidden words. (This is joint work with Maxime Crochemore and Gabriele Fici).