Abstract Randomness on full shift spaces q

We give various characterizations for algorithmically random con®gurations on full shift spaces, based on randomness tests. We show that all nonsurjective cellular automata destroy randomness and surjective cellular automata preserve randomness. Furthermore all one-dimensional cellular automata preserve nonrandomness. The last three assertions are also true if one replaces randomness by richness ± a form of pseudorandomness, which is compatible with computability. The last assertion is true even for an arbitrar