7,000 research outputs found
Terminating population protocols via some minimal global knowledge assumptions
We extend the population protocol model with a cover-time service that informs a walking state every time it covers the whole network. This represents a known upper bound on the cover time of a random walk. The cover-time service allows us to introduce termination into population protocols, a capability that is crucial for any distributed system. By reduction to an oracle-model we arrive at a very satisfactory lower bound on the computational power of the model: we prove that it is at least as strong as a Turing Machine of space log n with input commutativity, where n is the number of nodes in the network. We also give a log n-space, but nondeterministic this time, upper bound. Finally, we prove interesting similarities of this model to linear bounded automata. Keywords: population protocol, cover-time service, rendezvous-based communication, interaction, counter machine, absence detector, linear-bounded automaton 1
Connectivity preserving network transformers
The Population Protocol model is a distributed model that concerns systems of
very weak computational entities that cannot control the way they interact. The
model of Network Constructors is a variant of Population Protocols capable of
(algorithmically) constructing abstract networks. Both models are characterized
by a fundamental inability to terminate. In this work, we investigate the
minimal strengthenings of the latter that could overcome this inability. Our
main conclusion is that initial connectivity of the communication topology
combined with the ability of the protocol to transform the communication
topology plus a few other local and realistic assumptions are sufficient to
guarantee not only termination but also the maximum computational power that
one can hope for in this family of models. The technique is to transform any
initial connected topology to a less symmetric and detectable topology without
ever breaking its connectivity during the transformation. The target topology
of all of our transformers is the spanning line and we call Terminating Line
Transformation the corresponding problem. We first study the case in which
there is a pre-elected unique leader and give a time-optimal protocol for
Terminating Line Transformation. We then prove that dropping the leader without
additional assumptions leads to a strong impossibility result. In an attempt to
overcome this, we equip the nodes with the ability to tell, during their
pairwise interactions, whether they have at least one neighbor in common.
Interestingly, it turns out that this local and realistic mechanism is
sufficient to make the problem solvable. In particular, we give a very
efficient protocol that solves Terminating Line Transformation when all nodes
are initially identical. The latter implies that the model computes with
termination any symmetric predicate computable by a Turing Machine of space
Connectivity Preserving Network Transformers
The Population Protocol model is a distributed model that concerns systems of
very weak computational entities that cannot control the way they interact. The
model of Network Constructors is a variant of Population Protocols capable of
(algorithmically) constructing abstract networks. Both models are characterized
by a fundamental inability to terminate. In this work, we investigate the
minimal strengthenings of the latter that could overcome this inability. Our
main conclusion is that initial connectivity of the communication topology
combined with the ability of the protocol to transform the communication
topology plus a few other local and realistic assumptions are sufficient to
guarantee not only termination but also the maximum computational power that
one can hope for in this family of models. The technique is to transform any
initial connected topology to a less symmetric and detectable topology without
ever breaking its connectivity during the transformation. The target topology
of all of our transformers is the spanning line and we call Terminating Line
Transformation the corresponding problem. We first study the case in which
there is a pre-elected unique leader and give a time-optimal protocol for
Terminating Line Transformation. We then prove that dropping the leader without
additional assumptions leads to a strong impossibility result. In an attempt to
overcome this, we equip the nodes with the ability to tell, during their
pairwise interactions, whether they have at least one neighbor in common.
Interestingly, it turns out that this local and realistic mechanism is
sufficient to make the problem solvable. In particular, we give a very
efficient protocol that solves Terminating Line Transformation when all nodes
are initially identical. The latter implies that the model computes with
termination any symmetric predicate computable by a Turing Machine of space
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
Simple and Efficient Local Codes for Distributed Stable Network Construction
In this work, we study protocols so that populations of distributed processes
can construct networks. In order to highlight the basic principles of
distributed network construction we keep the model minimal in all respects. In
particular, we assume finite-state processes that all begin from the same
initial state and all execute the same protocol (i.e. the system is
homogeneous). Moreover, we assume pairwise interactions between the processes
that are scheduled by an adversary. The only constraint on the adversary
scheduler is that it must be fair. In order to allow processes to construct
networks, we let them activate and deactivate their pairwise connections. When
two processes interact, the protocol takes as input the states of the processes
and the state of the their connection and updates all of them. Initially all
connections are inactive and the goal is for the processes, after interacting
and activating/deactivating connections for a while, to end up with a desired
stable network. We give protocols (optimal in some cases) and lower bounds for
several basic network construction problems such as spanning line, spanning
ring, spanning star, and regular network. We provide proofs of correctness for
all of our protocols and analyze the expected time to convergence of most of
them under a uniform random scheduler that selects the next pair of interacting
processes uniformly at random from all such pairs. Finally, we prove several
universality results by presenting generic protocols that are capable of
simulating a Turing Machine (TM) and exploiting it in order to construct a
large class of networks.Comment: 43 pages, 7 figure
Terminating Distributed Construction of Shapes and Patterns in a Fair Solution of Automata
In this work, we consider a solution of automata similar to Population Protocols and Network Constructors. The au-tomata, also called nodes, move passively in a well-mixed solution and can cooperate by interacting in pairs. Dur-ing every such interaction, the nodes, apart from updating their states, may also choose to connect to each other in order to start forming some required structure. The model introduced here is a more applied version of Network Con-structors, imposing geometrical constraints on the permissi-ble connections. Each node can connect to other nodes only via a very limited number of local ports, which implies that at any given time it has only a bounded number of neigh-bors. Connections are always made at unit distance and are perpendicular to connections of neighboring ports. Thoug
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
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