Passively mobile communicating machines that use restricted space

Abstract

We propose a new theoretical model for passively mobile Wireless Sensor Networks, called P M , standing for Passively mobile Machines. The main modification w.r.t. the Population Protocol model is that the 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 interaction graphs and define the complexity classes PM-SPACE(f (n)) parametrically, consisting of all predicates that are stably computable by some PM protocol that uses O(f (n)) memory in each agent. We provide a protocol that generates unique identifiers from scratch only by using O(log n) memory, and use it to provide an exact characterization of the classes PMSPACE(f (n)) when f (n) = Ω(log n): they are precisely the classes of all symmetric predicates in NSPACE(nf (n)). As a consequence, we obtain a space hierarchy of the PM model when the memory bounds are Ω(log n). Finally, we establish that the minimal space requirement for the computation of non-semilinear predicates is O(log log n).

Homonym Population Protocols

“…We now show how previous constructions improve the results about the passively mobile protocol model [7]. This section treats the case where S(n) = O(log log n) in the passively mobile protocol model.…”

“…Among many variants of population protocols, the passively mobile (logarithmic space) machine model introduced by Chatzigiannakis et al [7] generalizes the population protocol model where finite state agents are replaced by agents that correspond to arbitrary Turing machines with O(S(n)) space peragent, where n is the number of agents. An exact characterization [7] of computable predicates is given: this model can compute all symmetric predicates in N SP ACE(nS(n)) as long as S(n) = Ω(log n).…”

“…An exact characterization [7] of computable predicates is given: this model can compute all symmetric predicates in N SP ACE(nS(n)) as long as S(n) = Ω(log n). Chatzigiannakis et al establish that the model with a space in agent in S(n) = o(log log n) is equivalent to population protocols, i.e.…”

“…In particular, Chatzigiannakis et al [7] solved the cases S(n) = o(log log n) (equivalent to population protocols) and S(n) = O(log n) (equivalent to Turing machines). We provide a characterization for the case S(n) = O(log log n): the model is equivalent to k∈N SN SP ACE(log k n) (see Table 2).…”

Terminating distributed construction of shapes and patterns in a fair solution of automata

“…Finitestate processes on a complete interaction network, i.e., one in which every pair of processes may interact, (and several variations) compute the semilinear predicates [3]. Semilinearity persists up to o(log log n) local space but not more than this [13]. If, additionally, the connections between processes can hold a state from a finite domain (note that this is a stronger requirement than the on/off that the present work assumes) then the computational power dramatically increases to the commutative subclass of NSPACE(n 2 ) [30].…”