Dual state time: only input state and output state if the universe transition function exist. Global single state time: the universe transition function alters the present state in-place all at once. Local single state time: only one bit changes at a time.
Yes, that was an idea I remember having come up in discussions with both Tommaso Bolognesi and Stephen Wolfram: one local read/write head, vs. many local ones, vs. one global operator. To make a difference, it appears the many must be asynchronous, based on their intrinsic state?