Self-similar Functions and Population Protocols: A Characterization and a Comparison

Chandy et al. proposed the methodology of “self-similar algorithms” for distributed computation in dynamic environments. We further characterize the class of functions computable by such algorithms by showing that self-similarity induces an additive relationship among the level-sets of such functions. Angluin et al. introduced the population protocol model for computation in mobile sensor networks and characterized the class of predicates computable in a standard population. We define and characterize the class of self-similar predicates and show when they are computable by a population protocol.