Flat holonomies on automata networks

Abstract

We consider asynchronous dynamic networks of identical finite (independent of the network size) automata. A useful data structure on such networks is a partial orientation of its edges. It needs to be straight, i.e. have null holonomy (the difference between the number of up and down edges in each cycle). It also needs to be centered, i.e., have a unique node with no down edges. Using such orientation, any feasible computational task can be efficiently implemented with self-stabilization and synchronization. There are (interdependent) self-stabilizing asynchronous finite automata protocols that straighten and centralize any orientation. Such protocols may vary in assorted efficiency parameters and it is desirable to have each replaceable with any alternative responsible for a simple limited task. We describe an efficient reduction of any computational task to any set of such protocols compliant with our interface conditions. © Springer-Verlag Berlin Heidelberg 2006.