Abstract: In the near future, it is reasonable to expect that new types of systems will appear, of massive scale, expansive and permeating their environment, of very heterogeneous nature, and operating in a constantly changing networked environment. We expect that most such systems will have the form of a very large society of unimpressive networked artefacts. Yet by cooperation, they will be organized in large societies to accomplish tasks that are difficult or beyond the capabilities of todays conventional centralized systems.
The Population Protocol model of Angluin et. al. introduced a novel approach towards the study of such systems by assuming that each artefact is an agent, so limited, that can be represented as a finite-state sensor of constant (O(1)) total storage capacity. Such agents are passively mobile and communicate in pairs using a low-power wireless signal. It has been proven that, although such systems consist of extremely limited, cheap and bulk-produced hardware devices, they are still capable of carrying out very useful nontrivial computations. Based on this approach we investigate many new intriguing directions.

Abstract: The population protocol model (PP) proposed by Angluin et al. [2] describes sensor networks consisting of passively mobile finite-stateagents. The agents sense their environment and communicate in pairs to carry out some computation on the sensed values. The mediated population protocol model (MPP) [13] extended the PP model by communication links equipped with a constant size buffer. The MPP model was proved in [13] to be stronger than the PP model. However, its most important contribution is that it provides us with the ability to devise optimizing protocols, approximation protocols and protocols that decide properties of the communication graph on which they run. The latter case, suggests a simplified model, the GDM model, that was formally defined and studied in [11]. GDM is a special case of MPP that captures MPP's ability to decide properties of the communication graph. Here we survey recent advances in the area initiated by the proposal of the PP model and at the same time we provide new protocols, novel ideas and results.

Abstract: We explore the capability of a network of extremely limited computational entities to decide properties about itself or any of its subnetworks. We consider that the underlying network of the interacting entities (devices, agents, processes etc.) is modeled by an interaction graph that reflects the network’s connectivity. We examine the following two cases: First, we consider the case where the input graph is the whole interaction graph and second where it is some subgraph of the interaction graph given by some preprocessing on the network. In each case, we devise simple graph protocols that can decide properties of the input graph. The computational entities, that are called agents, are modeled as finite-state automata and run the same global graph protocol. Each protocol is a fixed size grammar, that is, its description is independent of the size (number of agents) of the network. This size is not known by the agents. We present two simple models (one for each case), the Graph Decision Mediated Population Protocol (GDMPP) and the Mediated Graph Protocol (MGP) models, similar to the Population Protocol model of Angluin et al., where each network link (edge of the interaction graph) is characterized by a state taken from a finite set. This state can be used and updated during each interaction between the corresponding agents. We provide some example protocols and some interesting properties for the two models concerning the computability of graph languages in various settings (disconnected input graphs, stabilizing input graphs). We show that the computational power within the family of all (at least) weakly-connected input graphs is fairly restricted. Finally, we give an exact characterization of the class of graph languages decidable by the MGP model in the case of complete interaction graphs: it is equal to the class of graph languages decidable by a nondeterministic Turing Machine of linear space that receives its input graph by its adjacency matrix representation.