def METHOD_NAME(old_machine, debug=None):
    """
    Given a nondeterministic Machine, return a new equivalent
    Machine which is deterministic.
    """
    # We build a new machine whose states correspond to sets of states
    # in the old machine. Initially we add a new state corresponding to
    # the epsilon-closure of each initial old state. Then we give transitions
    # to each new state which are the union of all transitions out of any
    # of the corresponding old states. The new state reached on a given
    # character is the one corresponding to the set of states reachable
    # on that character from any of the old states. As new combinations of
    # old states are created, new states are added as needed until closure
    # is reached.
    new_machine = Machines.FastMachine()
    state_map = StateMap(new_machine)
    # Seed the process using the initial states of the old machine.
    # Make the corresponding new states into initial states of the new
    # machine with the same names.
    for (key, old_state) in old_machine.initial_states.items():
        new_state = state_map.old_to_new(epsilon_closure(old_state))
        new_machine.make_initial_state(key, new_state)
    # Tricky bit here: we add things to the end of this list while we're
    # iterating over it. The iteration stops when closure is achieved.
    for new_state in new_machine.states:
        transitions = TransitionMap()
        for old_state in state_map.new_to_old(new_state):
            for event, old_target_states in old_state.transitions.items():
                if event and old_target_states:
                    transitions.add_set(event, set_epsilon_closure(old_target_states))
        for event, old_states in transitions.items():
            new_machine.add_transitions(new_state, event, state_map.old_to_new(old_states))
    if debug:
        debug.write("\n===== State Mapping =====\n")
        state_map.dump(debug)
    return new_machine