2 research outputs found
Computing by Temporal Order: Asynchronous Cellular Automata
Our concern is the behaviour of the elementary cellular automata with state
set 0,1 over the cell set Z/nZ (one-dimensional finite wrap-around case), under
all possible update rules (asynchronicity).
Over the torus Z/nZ (n<= 11),we will see that the ECA with Wolfram rule 57
maps any v in F_2^n to any w in F_2^n, varying the update rule.
We furthermore show that all even (element of the alternating group)
bijective functions on the set F_2^n = 0,...,2^n-1, can be computed by ECA57,
by iterating it a sufficient number of times with varying update rules, at
least for n <= 10. We characterize the non-bijective functions computable by
asynchronous rules.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249