Νέα μοντέλα για πρωτόκολλα πληθυσμών

Abstract

Wireless Sensor Networks (WSNs) constitute a recent and promising new technology that is widely applicable. Due to the applicability of this technology and its obvious importance for the modern distributed computational world, the formal scientific foundation of its inherent laws becomes essential. As a result, many new computational models for WSNs have been proposed. Population Protocols (PPs) are a special category of such systems. These are mainly identified by three distinctive characteristics: the sensor nodes (agents) move passively, that is, they cannot control the underlying mobility pattern, the available memory to each agent is restricted, and the agents interact in pairs. It has been proven that a predicate is computable by the PP model iff it is semilinear. The class of semilinear predicates is a fairly small class. In this work, our basic goal is to enhance the PP model in order to improve the computational power. We first make the assumption that not only the nodes but also the edges of the communication graph can store restricted states. In a complete graph of n nodes it is like having added O(n^2) additional memory cells which are only read and written by the endpoints of the corresponding edge. We prove that the new model, called Mediated Population Protocol model, can operate as a distributed nondeterministic Turing machine (TM) that uses all the available memory. The only difference from a usual TM is that this one computes only symmetric languages. More formally, we establish that a predicate is computable by the new model iff it is symmetric and belongs to NSPACE(n^2). Moreover, we study the ability of the new model to decide graph languages (for general graphs). The next step is to ignore the states of the edges and provide another enhancement straight away from the PP model. The assumption now is that the agents are multitape TMs equipped with infinite memory, that can perform internal computation and interact with other agents, and we define space-bounded computations. We call this the Passively mobile Machines model. We prove that if each agent uses at most f(n) memory for f(n)=Ω(log n) then a predicate is computable iff it is symmetric and belongs to NSPACE(nf(n)). We also show that this is not the case for f(n)=o(log n). Based on these, we show that for f(n)=Ω(log n) there exists a space hierarchy like the one for classical symmetric TMs. We also show that the latter is not the case for f(n)=o(loglog n), since here the corresponding class collapses in the class of semilinear predicates and finally that for f(n)=Ω(loglog n) the class becomes a proper superset of semilinear predicates. We leave open the problem of characterizing the classes for f(n)=Ω(loglog n) and f(n)=o(log n).