def growth_matrices( automaton, initial_state ):
    """Returns 2 matrices: A,b,c, defining a discrete-time linear system whose impulse responce
    is number of accepted strings.
    """
    n  = automaton.num_states()
    a = [ [0 for _ in range(n)]
          for __ in range(n)]
    for state, state_transitions in enumerate(automaton.transitions ):
        for new_state in state_transitions.values():
            a[new_state][state] = 1
    b = [0]*n
    b[initial_state] = 1

    c = [1]*n
    return a,b,c