 
Summary: Fast Computation by Population Protocols With a
Leader
Dana Angluin1
, James Aspnes1
, and David Eisenstat2
1
Yale University, Department of Computer Science
2
Princeton University, Department of Computer Science
Abstract. Fast algorithms are presented for performing computations in a prob
abilistic population model. This is a variant of the standard population proto
col 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 ini
tial population, the population can simulate a virtual register machine in which
standard arithmetic operations like comparison, addition, subtraction, and multi
plication and division by constants 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
