# How Cellular Automata is related to Automata Theory?

I have read about Automata Theory where it is about the study of abstract machines and automata.

And i know that an abstract machine takes the input, process it and create the output, just like Conway's Game of life.

But, what a formal defination can relate it to Cellular Automata, what about Elementary Cellular Automata, can it related also?

• No relation other than the name and the finite number of states. – Yuval Filmus Oct 7 '15 at 5:31
• @YuvalFilmus that's actually not entirely true. I.e. cellular automata may have infinite number of states. I.e. instead of discrete values they may produce continuous output and have some real-valued function as their transition function. – wvxvw Oct 7 '15 at 7:54
• Actually, automata theory also makes use of automata with an infinite number of states. Here is an example: a subset of $A^\omega$ is closed iff it is accepted by a deterministic (possibly infinite) Bûchi automaton in which all states are final. – J.-E. Pin Oct 8 '15 at 8:26