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Title: Message Complexity of Population Protocols
The standard population protocol model assumes that when two agents interact, each observes the entire state of the other agent. We initiate the study of the message complexity for population protocols, where the state of an agent is divided into an externally-visible message and an internal component, where only the message can be observed by the other agent in an interaction. We consider the case of O(1) message complexity. When time is unrestricted, we obtain an exact characterization of the stably computable predicates based on the number of internal states s(n): If s(n) = o(n) then the protocol computes a semilinear predicate (unlike the original model, which can compute non-semilinear predicates with s(n) = O(log n)), and otherwise it computes a predicate decidable by a nondeterministic O(n log s(n))-space-bounded Turing machine. We then consider time complexity, introducing novel O(polylog(n)) expected time protocols for junta/leader election and general purpose broadcast correct with high probability, and approximate and exact population size counting correct with probability 1. Finally, we show that the main constraint on the power of bounded-message-size protocols is the size of the internal states: with unbounded internal states, any computable function can be computed with probability 1 in the limit by more » a protocol that uses only one-bit messages. « less
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Attiya, Hagit
Award ID(s):
1650596 1900931 1844976
Publication Date:
Journal Name:
34th International Symposium on Distributed Computing, DISC 2020, October 12-16, 2020, Virtual Conference
Page Range or eLocation-ID:
Sponsoring Org:
National Science Foundation
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