Finite State Automata

Does everyone know what a Finite State Automaton is?
Imagine a simulation that is a bit more sophisticated than a categoriser.
In addition to the categoriser, there is another subsystem that encodes state.
As CAs can persist indefinitely, the state can be encoded by a CA. (You can use multiple CAs for a state. Indefinite persistence is easy to simulate, it's memory decay that is currently unsolved.)
For the system to move to the next state, it takes the current state, and the input, and transits.
More explicitly, say the current state is S0, the next state is S1, and the input is I0.
Inputs from S0 are insufficient to ignite S1 as are those from I0.
Together S0 and I0 can ignite S1. Is that reasonable?
S1 inhibits S0, so it turns it off.
That's all you need for an FSA.
That means you can parse regular languages.