This work focuses on the set of 32 legal Elementary Cellular Automata. We perform an exhaustive study of the systems' response under: (i) α-asynchronous dynamics, from full asynchronism to perfect synchrony; (ii) Φ-noise scheme, a perturbation that causes a cell to miscalculate the new state when it is updated. We propose a new classification in three classes under asynchronous conditions: α-invariant, α-robust and α-dependent. We classify the 32 legal automata according to the degree of behavioural modification. We demonstrate that, in the α-dependent class, asynchrony behaves as a form of noise in timing. We identify models tolerant to both noise and asynchrony. While the majority of the a-invariant class is robust to noise, a subset is not able to recover its original behaviour.
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