122,437 research outputs found
Counting with Population Protocols
âThe population protocol model provides theoretical foundations for analyzing the properties emerging from simple and pairwise interactions among a very large number n of anonymous agents. The problem tackled in this paper is the following one: is there an efficient population protocol that exactly counts the difference Îș between the number of agents that initially and independently set their state to A and the one that initially set it to B, assuming that each agent only uses a finite set of states ? We propose a solution which guarantees with any high probability that after O (log n) interactions any agent outputs the exact value of Îș. Simulation results illustrate our theoretical analysis
Population Protocols with Unordered Data
Population protocols form a well-established model of computation of passively mobile anonymous agents with constant-size memory. It is well known that population protocols compute Presburger-definable predicates, such as absolute majority and counting predicates. In this work, we initiate the study of population protocols operating over arbitrarily large data domains. More precisely, we introduce population protocols with unordered data as a formalism to reason about anonymous crowd computing over unordered sequences of data. We first show that it is possible to determine whether an unordered sequence from an infinite data domain has a datum with absolute majority. We then establish the expressive power of the "immediate observation" restriction of our model, namely where, in each interaction, an agent observes another agent who is unaware of the interaction
Population Protocols with Unordered Data
Population protocols form a well-established model of computation of
passively mobile anonymous agents with constant-size memory. It is well known
that population protocols compute Presburger-definable predicates, such as
absolute majority and counting predicates. In this work, we initiate the study
of population protocols operating over arbitrarily large data domains. More
precisely, we introduce population protocols with unordered data as a formalism
to reason about anonymous crowd computing over unordered sequences of data. We
first show that it is possible to determine whether an unordered sequence from
an infinite data domain has a datum with absolute majority. We then establish
the expressive power of the immediate observation restriction of our model,
namely where, in each interaction, an agent observes another agent who is
unaware of the interaction.Comment: accepted at ICALP 202
NETCS: A New Simulator of Population Protocols and Network Constructors
Network Constructors are an extension of the standard population protocol model in which finite-state agents interact in pairs under the control of an adversary scheduler. In this work we present NETCS, a simulator designed to evaluate the performance of various network constructors and population protocols under different schedulers and network configurations. Our simulator provides researchers with an intuitive user interface and a quick experimentation environment to evaluate their work. It also harnesses the power of the cloud, as experiments are executed remotely and scheduled through the web interface provided. To prove the validity and quality of our simulator we provide an extensive evaluation of multiple protocols with more than 100000 experiments for different network sizes and configurations that validate the correctness of the theoretical analysis of existing protocols and estimate the real values of the hidden asymptotic coefficients. We also show experimentally (with more than 40000 experiments) that a probabilistic algorithm is capable of counting the actual size of the network in bounded time given a unique leader
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
for population protocols, where the state of an
agent is divided into an externally-visible and an internal
component, where only the message can be observed by the other agent in an
interaction.
We consider the case of message complexity. When time is unrestricted,
we obtain an exact characterization of the stably computable predicates based
on the number of internal states : If then the protocol
computes semilinear predicates (unlike the original model, which can compute
non-semilinear predicates with ), and otherwise it computes a
predicate decidable by a nondeterministic -space-bounded Turing
machine. We then introduce novel 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 a protocol that uses only
messages
Uniform Partition in Population Protocol Model Under Weak Fairness
We focus on a uniform partition problem in a population protocol model. The uniform partition problem aims to divide a population into k groups of the same size, where k is a given positive integer. In the case of k=2 (called uniform bipartition), a previous work clarified space complexity under various assumptions: 1) an initialized base station (BS) or no BS, 2) weak or global fairness, 3) designated or arbitrary initial states of agents, and 4) symmetric or asymmetric protocols, except for the setting that agents execute a protocol from arbitrary initial states under weak fairness in the model with an initialized base station. In this paper, we clarify the space complexity for this remaining setting. In this setting, we prove that P states are necessary and sufficient to realize asymmetric protocols, and that P+1 states are necessary and sufficient to realize symmetric protocols, where P is the known upper bound of the number of agents. From these results and the previous work, we have clarified the solvability of the uniform bipartition for each combination of assumptions. Additionally, we newly consider an assumption on a model of a non-initialized BS and clarify solvability and space complexity in the assumption. Moreover, the results in this paper can be applied to the case that k is an arbitrary integer (called uniform k-partition)
Efficient size estimation and impossibility of termination in uniform dense population protocols
We study uniform population protocols: networks of anonymous agents whose
pairwise interactions are chosen at random, where each agent uses an identical
transition algorithm that does not depend on the population size . Many
existing polylog time protocols for leader election and majority
computation are nonuniform: to operate correctly, they require all agents to be
initialized with an approximate estimate of (specifically, the exact value
). Our first main result is a uniform protocol for
calculating with high probability in time and
states ( bits of memory). The protocol is
converging but not terminating: it does not signal when the estimate is close
to the true value of . If it could be made terminating, this would
allow composition with protocols, such as those for leader election or
majority, that require a size estimate initially, to make them uniform (though
with a small probability of failure). We do show how our main protocol can be
indirectly composed with others in a simple and elegant way, based on the
leaderless phase clock, demonstrating that those protocols can in fact be made
uniform. However, our second main result implies that the protocol cannot be
made terminating, a consequence of a much stronger result: a uniform protocol
for any task requiring more than constant time cannot be terminating even with
probability bounded above 0, if infinitely many initial configurations are
dense: any state present initially occupies agents. (In particular,
no leader is allowed.) Crucially, the result holds no matter the memory or time
permitted. Finally, we show that with an initial leader, our size-estimation
protocol can be made terminating with high probability, with the same
asymptotic time and space bounds.Comment: Using leaderless phase cloc
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