This is a follow-up to the question Undecidability in Conway’s Game of Life I posted at mathoverflow.
For some cellular automata it can be proven that they can simulate a Turing machine, normally by explicit construction. For some of them it can be proven that they can not simulate a Turing machine.
Are there computable sufficient conditions on a cellular automaton to be Turing-complete (besides of being one of the known cases)? (My guess is: No.)
If not: Why not?
If not: Can non-computable sufficient conditions be named?
What about necessary conditions?
What's the "standard" way of showing that a cellular automaton is not Turing-complete?
I recently read this paper that seems related to your question "Communication Complexity and Intrinsic Universality in Cellular Automata"
There are some classes of cellular automatas (having some decidable properties) for which non-turing completeness can be proved.