We consider the model of population protocols introduced by Angluin et al. (Computation in networks of passively mobile finite-state sensors, pp. 290-299. ACM, New York, 2004), in which anonymous finite-state agents stably compute a predicate of the multiset of their inputs via two-way interactions in the family of all-pairs communication networks. We prove that all predicates stably computable in this model (and certain generalizations of it) are semilinear, answering a central open question about the power of the model. Removing the assumption of two-way interaction, we also consider several variants of the model in which agents communicate by anonymous message-passing where the recipient of each message is chosen by an adversary and the sender is not identified to the recipient. These one-way models are distinguished by whether messages are delivered immediately or after a delay, whether a sender can record that it has sent a message, and whether a recipient can queue James Aspnes was supported in part by NSF grants CNS-0305258 and incoming messages, refusing to accept new messages until it has had a chance to send out messages of its own. We characterize the classes of predicates stably computable in each of these one-way models using natural subclasses of the semilinear predicates.

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The population protocol model describes a collection of tiny mobile agents that interact with one another to carry out a computation. The agents are identically programmed finite state machines. Interactions between pairs of agents cause the two agents to update their states. These interactions are scheduled by an adversary, subject to a fairness constraint. Input values are initially distributed to the agents, and the agents must eventually converge to the correct output value. This framework can be used to model mobile ad hoc networks of tiny devices or collections of molecules undergoing chemical reactions. We survey results that describe what can be computed in various versions of the population protocol model.

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We describe a general technique for obtaining provably correct, non-blocking implementations of a large class of tree data structures where pointers are directed from parents to children. Updates are permitted to modify any contiguous portion of the tree atomically. Our non-blocking algorithms make use of the LLX, SCX and VLX primitives, which are multi-word generalizations of the standard LL, SC and VL primitives and have been implemented from single-word CAS [10].To illustrate our technique, we describe how it can be used in a fairly straightforward way to obtain a non-blocking implementation of a chromatic tree, which is a relaxed variant of a red-black tree. The height of the tree at any time is O(c + log n), where n is the number of keys and c is the number of updates in progress. We provide an experimental performance analysis which demonstrates that our Java implementation of a chromatic tree rivals, and often significantly outperforms, other leading concurrent dictionaries.

We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, fault-tolerance, different communication media, and randomization. The resource bounds refer to time, space and message complexity. These results are useful in understanding the inherent difficulty of individual problems and in studying the power of different models of distributed computing. There is a strong emphasis in our presentation on explaining the wide variety of techniques that are used to obtain the results described.

Abstract. We introduce a new theoretical model of ad hoc mobile computing in which agents have severely restricted memory, highly unpredictable movement and no initial knowledge of the system. Each agent's memory can store O(1) bits, plus a unique identifier, and O(1) other agents' identifiers. Inputs are distributed across n agents, and all agents must converge to the correct output value. We give a universal construction that proves the model is surprisingly strong: It can solve any decision problem in N SP ACE(n log n). Moreover, the construction is robust with respect to Byzantine failures of a constant number of agents.

In the population protocol model introduced by Angluin et al.[2], a collection of agents, which are modelled by finite state machines, move around unpredictably and have pairwise interactions. The ability of such systems to compute functions on a multiset of inputs that are initially distributed across all of the agents has been studied in the absence of failures. Here, we show that essentially the same set of functions can be computed in the presence of halting and transient failures, provided preconditions on the inputs are added so that the failures cannot immediately obscure enough of the inputs to change the outcome. We do this by giving a general-purpose transformation that makes any algorithm for the fault-free setting tolerant to failures.