 
Summary: Selfstabilizing Population Protocols
Dana Angluin, James Aspnes , Michael J. Fischer, and Hong Jiang
Yale University, Department of Computer Science
Abstract. Selfstabilization in a model of anonymous, asynchronous interact
ing agents deployed in a network of unknown size is considered. Dijkstrastyle
roundrobin token circulation can be done deterministically with constant space
per node in this model. Constantspace protocols are given for leader election
in rings, localaddressing in degreebounded graphs, and establishing consistent
global direction in an undirected ring. A protocol to construct a spanning tree in
regular graphs using O(log D) memory is also given, where D is the diameter
of the graph. A general method for eliminating nondeterministic transitions from
the selfstabilizing implementation of a large family of behaviors is used to sim
plify the constructions, and general conditions under which protocol composition
preserves behavior are used in proving their correctness.
1 Introduction
In some practical scenarios, a large (and sometimes unknown) number of devices are
deployed over a certain region without fine control of their locations, communication
and movement patterns. The devices are all indistinguishable and have only a few bits
of memory each. Such scenarios are modeled by the population protocols introduced
in [1], where families of predicates computable in this model are explored. Graph prop
