15 research outputs found

    Mediated population protocols

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    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

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    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

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    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

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    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 O(nlogkn)O(n\log^k n), 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 (ab)(ab)^*, are not computable.Comment: Long version of SSS 2016 publication, appendixed version of SIROCCO 201

    Terminating population protocols via some minimal global knowledge assumptions

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    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

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    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 Θ(n2)\Theta(n^2)

    Connectivity Preserving Network Transformers

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    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 Θ(n2)\Theta(n^2)

    Population protocols with faulty interactions: The impact of a leader

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    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
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