15 research outputs found
Mediated population protocols
We extend here the Population Protocol (PP) model of Angluin et al. (2004, 2006) [2,4] in order to model more powerful networks of resource-limited agents that are possibly mobile. The main feature of our extended model, called the Mediated Population Protocol (MPP) model, is to allow the edges of the interaction graph to have states that belong to a constant-size set. We then allow the protocol rules for pairwise interactions to modify the corresponding edge state. The descriptions of our protocols preserve both the uniformity and anonymity properties of PPs, that is, they do not depend on the size of the population and do not use unique identifiers. We focus on the computational power of the MPP model on complete interaction graphs and initially identical edges. We provide the following exact characterization of the class MPS of stably computable predicates: a predicate is in MPS iff it is symmetric and is in NSPACE(n2). © 2010 Elsevier B.V. All rights reserved
Passively Mobile Communicating Logarithmic Space Machines
We propose a new theoretical model for passively mobile Wireless Sensor
Networks. We call it the PALOMA model, standing for PAssively mobile
LOgarithmic space MAchines. The main modification w.r.t. the Population
Protocol model is that agents now, instead of being automata, are Turing
Machines whose memory is logarithmic in the population size n. Note that the
new model is still easily implementable with current technology. We focus on
complete communication graphs. We define the complexity class PLM, consisting
of all symmetric predicates on input assignments that are stably computable by
the PALOMA model. We assume that the agents are initially identical.
Surprisingly, it turns out that the PALOMA model can assign unique consecutive
ids to the agents and inform them of the population size! This allows us to
give a direct simulation of a Deterministic Turing Machine of O(nlogn) space,
thus, establishing that any symmetric predicate in SPACE(nlogn) also belongs to
PLM. We next prove that the PALOMA model can simulate the Community Protocol
model, thus, improving the previous lower bound to all symmetric predicates in
NSPACE(nlogn). Going one step further, we generalize the simulation of the
deterministic TM to prove that the PALOMA model can simulate a Nondeterministic
TM of O(nlogn) space. Although providing the same lower bound, the important
remark here is that the bound is now obtained in a direct manner, in the sense
that it does not depend on the simulation of a TM by a Pointer Machine.
Finally, by showing that a Nondeterministic TM of O(nlogn) space decides any
language stably computable by the PALOMA model, we end up with an exact
characterization for PLM: it is precisely the class of all symmetric predicates
in NSPACE(nlogn).Comment: 22 page
Passively mobile communicating machines that use restricted space
We propose a new theoretical model for passively mobile Wireless Sensor Networks, called PM, standing for Passively mobile Machines. The main modification w.r.t. the Population Protocol model [Angluin et al. 2006] is that the agents now, instead of being automata, are Turing Machines. We provide general definitions for unbounded memories, but we are mainly interested in computations upper-bounded by plausible space limitations. However, we prove that our results hold for more general cases. We focus on complete interaction graphs and define the complexity classes PM-SPACE(f(n)) parametrically, consisting of all predicates that are stably computable by some PM protocol that uses O(f(n)) memory in each agent. We provide a protocol that generates unique identifiers from scratch only by using O(log n) memory, and use it to provide an exact characterization of the classes PMSPACE(f(n)) when f(n) = Ω(log n): they are precisely the classes of all symmetric predicates in NSPACE(nf(n)). As a consequence, we obtain a space hierarchy of the PM model when the memory bounds are Ω(log n). Finally, we establish that the minimal space requirement for the computation of non-semilinear predicates is O(log log n). © 2011 ACM.FOM
Global Versus Local Computations: Fast Computing with Identifiers
This paper studies what can be computed by using probabilistic local
interactions with agents with a very restricted power in polylogarithmic
parallel time. It is known that if agents are only finite state (corresponding
to the Population Protocol model by Angluin et al.), then only semilinear
predicates over the global input can be computed. In fact, if the population
starts with a unique leader, these predicates can even be computed in a
polylogarithmic parallel time. If identifiers are added (corresponding to the
Community Protocol model by Guerraoui and Ruppert), then more global predicates
over the input multiset can be computed. Local predicates over the input sorted
according to the identifiers can also be computed, as long as the identifiers
are ordered. The time of some of those predicates might require exponential
parallel time. In this paper, we consider what can be computed with Community
Protocol in a polylogarithmic number of parallel interactions. We introduce the
class CPPL corresponding to protocols that use , for some k,
expected interactions to compute their predicates, or equivalently a
polylogarithmic number of parallel expected interactions. We provide some
computable protocols, some boundaries of the class, using the fact that the
population can compute its size. We also prove two impossibility results
providing some arguments showing that local computations are no longer easy:
the population does not have the time to compare a linear number of consecutive
identifiers. The Linearly Local languages, such that the rational language
, are not computable.Comment: Long version of SSS 2016 publication, appendixed version of SIROCCO
201
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
Population protocols with faulty interactions: The impact of a leader
We consider the problem of simulating traditional popula-tion protocols under weaker models of communication, which include one-way interactions (as opposed to two-way interactions) and omission faults (i.e., failure by an agent to read its partner’s state during an inter-action), which in turn may be detectable or undetectable. We focus on the impact of a leader, and we give a complete characterization of the models in which the presence of a unique leader in the system allows the construction of simulators: when simulations are possible, we give explicit protocols; when they are not, we give proofs of impossibility. Specifically, if each agent has only a finite amount of memory, the simulation is pos-sible only if there are no omission faults. If agents have an unbounded amount of memory, the simulation is possible as long as omissions are detectable. If an upper bound on the number of omissions involving the leader is known, the simulation is always possible, except in the one-way model in which one side is unable to detect the interaction