40 research outputs found
Mediated population protocols
We extend here the Population Protocol (PP) model of Angluin et al. (2004, 2006) [2,4] in order to model more powerful networks of resource-limited agents that are possibly mobile. The main feature of our extended model, called the Mediated Population Protocol (MPP) model, is to allow the edges of the interaction graph to have states that belong to a constant-size set. We then allow the protocol rules for pairwise interactions to modify the corresponding edge state. The descriptions of our protocols preserve both the uniformity and anonymity properties of PPs, that is, they do not depend on the size of the population and do not use unique identifiers. We focus on the computational power of the MPP model on complete interaction graphs and initially identical edges. We provide the following exact characterization of the class MPS of stably computable predicates: a predicate is in MPS iff it is symmetric and is in NSPACE(n2). © 2010 Elsevier B.V. All rights reserved
Passively Mobile Communicating Logarithmic Space Machines
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 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(nlogn) space,
thus, establishing that any symmetric predicate in SPACE(nlogn) also belongs to
PLM. We next prove that the PALOMA model can simulate the Community Protocol
model, thus, improving the previous lower bound to all symmetric predicates in
NSPACE(nlogn). 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(nlogn) 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(nlogn) 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(nlogn).Comment: 22 page
Shortest, Fastest, and Foremost Broadcast in Dynamic Networks
Highly dynamic networks rarely offer end-to-end connectivity at a given time.
Yet, connectivity in these networks can be established over time and space,
based on temporal analogues of multi-hop paths (also called {\em journeys}).
Attempting to optimize the selection of the journeys in these networks
naturally leads to the study of three cases: shortest (minimum hop), fastest
(minimum duration), and foremost (earliest arrival) journeys. Efficient
centralized algorithms exists to compute all cases, when the full knowledge of
the network evolution is given.
In this paper, we study the {\em distributed} counterparts of these problems,
i.e. shortest, fastest, and foremost broadcast with termination detection
(TDB), with minimal knowledge on the topology.
We show that the feasibility of each of these problems requires distinct
features on the evolution, through identifying three classes of dynamic graphs
wherein the problems become gradually feasible: graphs in which the
re-appearance of edges is {\em recurrent} (class R), {\em bounded-recurrent}
(B), or {\em periodic} (P), together with specific knowledge that are
respectively (the number of nodes), (a bound on the recurrence
time), and (the period). In these classes it is not required that all pairs
of nodes get in contact -- only that the overall {\em footprint} of the graph
is connected over time.
Our results, together with the strict inclusion between , , and ,
implies a feasibility order among the three variants of the problem, i.e.
TDB[foremost] requires weaker assumptions on the topology dynamics than
TDB[shortest], which itself requires less than TDB[fastest]. Reversely, these
differences in feasibility imply that the computational powers of ,
, and also form a strict hierarchy
Towards Efficient Verification of Population Protocols
Population protocols are a well established model of computation by
anonymous, identical finite state agents. A protocol is well-specified if from
every initial configuration, all fair executions reach a common consensus. The
central verification question for population protocols is the
well-specification problem: deciding if a given protocol is well-specified.
Esparza et al. have recently shown that this problem is decidable, but with
very high complexity: it is at least as hard as the Petri net reachability
problem, which is EXPSPACE-hard, and for which only algorithms of non-primitive
recursive complexity are currently known.
In this paper we introduce the class WS3 of well-specified strongly-silent
protocols and we prove that it is suitable for automatic verification. More
precisely, we show that WS3 has the same computational power as general
well-specified protocols, and captures standard protocols from the literature.
Moreover, we show that the membership problem for WS3 reduces to solving
boolean combinations of linear constraints over N. This allowed us to develop
the first software able to automatically prove well-specification for all of
the infinitely many possible inputs.Comment: 29 pages, 1 figur
Simple and Efficient Local Codes for Distributed Stable Network Construction
In this work, we study protocols so that populations of distributed processes
can construct networks. In order to highlight the basic principles of
distributed network construction we keep the model minimal in all respects. In
particular, we assume finite-state processes that all begin from the same
initial state and all execute the same protocol (i.e. the system is
homogeneous). Moreover, we assume pairwise interactions between the processes
that are scheduled by an adversary. The only constraint on the adversary
scheduler is that it must be fair. In order to allow processes to construct
networks, we let them activate and deactivate their pairwise connections. When
two processes interact, the protocol takes as input the states of the processes
and the state of the their connection and updates all of them. Initially all
connections are inactive and the goal is for the processes, after interacting
and activating/deactivating connections for a while, to end up with a desired
stable network. We give protocols (optimal in some cases) and lower bounds for
several basic network construction problems such as spanning line, spanning
ring, spanning star, and regular network. We provide proofs of correctness for
all of our protocols and analyze the expected time to convergence of most of
them under a uniform random scheduler that selects the next pair of interacting
processes uniformly at random from all such pairs. Finally, we prove several
universality results by presenting generic protocols that are capable of
simulating a Turing Machine (TM) and exploiting it in order to construct a
large class of networks.Comment: 43 pages, 7 figure