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(n2)
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(n2). 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)=Ù(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)=Ù(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)=Ù(loglog n) the class becomes a proper superset of semilinear
predicates. We leave open the problem of characterizing the classes for
f(n)=Ù(loglog n) and f(n)=o(log n). |