  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 is that 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 communication graphs and define the
complexity classes PMSPACE(f(n)) parametrically, consisting of all predicates
that are stably computable by some PM protocol that uses O(f(n)) memory on each
agent. We provide a protocol that generates unique ids from scratch only by
using O(log n) memory, and use it to provide an exact characterization for the
classes PMSPACE(f(n)) when f(n)={\Omega}(log n): they are precisely the classes
of all symmetric predicates in NSPACE(nf(n)). In this way, we provide a space
hierarchy for the PM model when the memory bounds are {\Omega}(log n). Finally,
we explore the computability of the PM model when the protocols use o(loglog n)
space per machine and prove that SEMILINEAR=PMSPACE(f(n)) when f(n)=o(loglog
n), where SEMILINEAR denotes the class of the semilinear predicates. In fact,
we prove that this bound acts as a threshold, so that SEMILINEAR is a proper
subset of PMSPACE(f(n)) when f(n)=O(loglog n).
