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?