Associating parallel automata network dynamics and strictly one-way cellular automata

We prove that the limit dynamics of any finite automata network under the parallel update schedule correspond exactly to the fixed points of a so-called strictly one-way cellular automaton. This correspondence is proven to be exact, as any strictly one-way cellular automaton can be transformed into a corresponding automata network, the limit dynamics of the latter corresponding exactly to the fixed points of the former. This transformation is operated using output functions, which have been developed in the author's previous works.

Automated summary

This paper proves the exact correspondence between the limit dynamics of a finite automata network under the parallel update schedule and the fixed points of a strictly one-way cellular automaton. The transformation from a strictly one-way cellular automaton to a corresponding automata network is accomplished using output functions developed in the author's previous works.