 
Summary: Yale University
Department of Computer Science
Fast Computation by Population Protocols With a Leader
Dana Angluin James Aspnes David Eisenstat
YALEU/DCS/TR1358
May 2006
Fast Computation by Population Protocols With a Leader
Dana Angluin
James Aspnes
David Eisenstat
Abstract
Fast algorithms are presented for performing computations in a probabilistic population model. This
is a variant of the standard population protocol modelin which finitestate agents interact in pairs
under the control of an adversary schedulerwhere all pairs are equally likely to be chosen for each
interaction. It is shown that when a unique leader agent is provided in the initial population, the popu
lation can simulate a virtual register machine in which standard arithmetic operations like comparison,
addition, subtraction, multiplication, and division can be simulated in O(n log4
n) interactions with
high probability. Applications include a reduction of the cost of computing a semilinear predicate to
O(n log4
