Abstract | We propose a new theoretical model for passively mobile Wireless Sensor Networks. We
call it the PALOMA model, standing for PAssively mobile LOgarithmic space MAchines. The main
modification w.r.t. the Population Protocol model [2] is that agents now, instead of being automata, are
Turing Machines whose memory is logarithmic in the population size n. Note that the new model is still
easily implementable with current technology. We focus on complete communication graphs. We define
the complexity class PLM, consisting of all symmetric predicates on input assignments that are stably
computable by the PALOMA model. We assume that the agents are initially identical. Surprisingly, it
turns out that the PALOMA model can assign unique consecutive ids to the agents and inform them
of the population size! This allows us to give a direct simulation of a Deterministic Turing Machine
of O(n log n) space, thus, establishing that any symmetric predicate in SPACE(n log n) also belongs
to PLM. We next prove that the PALOMA model can simulate the Community Protocol model [15],
thus, improving the previous lower bound to all symmetric predicates in NSPACE(n log n). Going
one step further, we generalize the simulation of the deterministic TM to prove that the PALOMA
model can simulate a Nondeterministic TM of O(n log n) space. Although providing the same lower
bound, the important remark here is that the bound is now obtained in a direct manner, in the sense
that it does not depend on the simulation of a TM by a Pointer Machine. Finally, by showing that a
Nondeterministic TM of O(n log n) space decides any language stably computable by the PALOMA
model, we end up with an exact characterization for PLM: it is precisely the class of all symmetric
predicates in NSPACE(n log n). |