Computation of functions on n bits by asynchronous clocking of cellular automata

Hard, firm, soft … Etherealware:Computing by Temporal Order of Clocking

“…permutations of the cells lead to different temporal rules. Their equivalence classes coincide-for our setting, CAs on the torus-with our result ( [10], Thm. 1]).…”

“…Here, continuing the work in [10,14], we again employ CAs as computing devices, whose work comes to an end, when the pattern transformation or function evaluation has been obtained. Also, the clocking, the temporal update rule, is completely deterministic and replaces the usual ways of representing an algorithm, either in software (initial data) or in hardware (choice of ECA and connecting graph).…”

“…We considered quad CAs (QCAs) with four inputs and nonstandard neighborhoods in ( [10], Section 1.2).…”

A Guided Tour of Asynchronous Cellular Automata

“…We also point out that Vielhaber has designed a formal framework in which the computations of functions on finite binary rings (Z/nZ) are made not by changing the local rule but by a proper use of the order of updating on a fixed rule [132]. In particular, he showed that ECA 57 with periodic boundary conditions was a rule especially adapted for such a purpose.…”

Asynchronous Cellular Automata

“…Similarly, an ordered updating may be simulated in a synchronous model by moving a token in a given order. However such direct transformations are not always possible: for example, Vielhaber has proposed an original way of achieving computation universality by selecting the cells to update [Vie13] and this construction cannot be transformed into a deterministic cellular automaton by the mere addition of a few internal states.…”