Abstract: Here we survey various computational models for Wireless Sensor Networks (WSNs). The population protocol model (PP) considers networks of tiny mobile finite-state artifacts that can sense the environment and communicate in pairs to perform a computation. The mediated population protocol model (MPP) enhances the previous model by allowing the communication links to have a constant size buffer, providing more computational power. The graph decision MPP model (GDM) is a special case of MPP that focuses on the MPP's ability to decide graph properties of the network. Another direction towards enhancing the PP is followed by the PALOMA model in which the artifacts are no longer finite-state automata but Turing Machines of logarithmic memory in the population size. A different approach to modeling WSNs is the static synchronous sensor field model (SSSF) which describes devices communicating through a fixed communication graph and interacting with their environment via input and output data streams. In this survey, we present the computational capabilities of each model and provide directions for further research.

Abstract: In this work, we consider a \emph{solution of automata} similar to \emph{Population Protocols} and \emph{Network Constructors}. The automata (also called \emph{nodes}) move passively in a well-mixed solution without being capable of controlling their movement. However, the nodes can \emph{cooperate} by interacting in pairs. Every such interaction may result in an update of the local states of the nodes. Additionally, the nodes may also choose to connect to each other in order to start forming some required structure. We may think of such nodes as the \emph{smallest possible programmable pieces of matter}, like tiny nanorobots or programmable molecules. The model that we introduce here is a more applied version of Network Constructors, imposing \emph{physical} (or \emph{geometrical}) \emph{constraints} on the connections that the nodes are allowed to form. Each node can connect to other nodes only via a very limited number of \emph{local ports}, which implies that at any given time it has only a \emph{bounded number of neighbors}. Connections are always made at \emph{unit distance} and are \emph{perpendicular to connections of neighboring ports}. Though such a model cannot form abstract networks like Network Constructors, it is still capable of forming very practical \emph{2D or 3D shapes}. We provide direct constructors for some basic shape construction problems, like \emph{spanning line}, \emph{spanning square}, and \emph{self-replication}. We then develop \emph{new techniques} for determining the computational and constructive capabilities of our model. One of the main novelties of our approach, concerns our attempt to overcome the inability of such systems to detect termination. In particular, we exploit the assumptions that the system is well-mixed and has a unique leader, in order to \emph{give terminating protocols that are correct with high probability}. This allows us to develop terminating subroutines that can be \emph{sequentially composed} to form larger \emph{modular protocols} (which has not been the case in the relevant literature). One of our main results is a \emph{terminating protocol counting the size $n$ of the system} with high probability. We then use this protocol as a subroutine in order to develop our \emph{universal constructors}, establishing that \emph{it is possible for the nodes to become self-organized with high probability into arbitrarily complex shapes while still detecting termination of the construction}.

Abstract: We explore the capability of a network of extremely limited
computational entities to decide properties about any of its subnetworks.
We consider that the underlying network of the interacting
entities (devices, agents, processes etc.) is modeled by a complete in-
teraction graph and we devise simple graph protocols that can decide
properties of some input subgraph provided by some preprocessing on
the network. The agents are modeled as nite-state automata and run
the same global graph protocol. Each protocol is a xed size grammar,
that is, its description is independent of the size (number of agents) of
the network. This size is not known by the agents. We propose a simple
model, the Mediated Graph Protocol (MGP) model, similar to the Population
Protocol model of Angluin et al., in which each network link is
characterized by a state taken from a nite set. This state can be used
and updated during each interaction between the corresponding agents.
We provide some interesting properties of the MGP model among which
is the ability to decide properties on stabilizing (initially changing for a
nite number of steps) input graphs and we show that the MGP model
has the ability to decide properties of disconnected input graphs. We
show that the computational power within the connected components is
fairly restricted. Finally, we give an exact characterization of the class
GMGP, of graph languages decidable by the MGP model: it is equal
to the class of graph languages decidable by a nondeterministic Turing
Machine of linear space that receives its input graph by its adjacency
matrix representation.

Abstract: We explore the capability of a network of extremely limited computational entities to decide properties about itself or any of its subnetworks. We consider that the underlying network of the interacting entities (devices, agents, processes etc.) is modeled by an interaction graph that reflects the network’s connectivity. We examine the following two cases: First, we consider the case where the input graph is the whole interaction graph and second where it is some subgraph of the interaction graph given by some preprocessing on the network. In each case, we devise simple graph protocols that can decide properties of the input graph. The computational entities, that are called agents, are modeled as finite-state automata and run the same global graph protocol. Each protocol is a fixed size grammar, that is, its description is independent of the size (number of agents) of the network. This size is not known by the agents. We present two simple models (one for each case), the Graph Decision Mediated Population Protocol (GDMPP) and the Mediated Graph Protocol (MGP) models, similar to the Population Protocol model of Angluin et al., where each network link (edge of the interaction graph) is characterized by a state taken from a finite set. This state can be used and updated during each interaction between the corresponding agents. We provide some example protocols and some interesting properties for the two models concerning the computability of graph languages in various settings (disconnected input graphs, stabilizing input graphs). We show that the computational power within the family of all (at least) weakly-connected input graphs is fairly restricted. Finally, we give an exact characterization of the class of graph languages decidable by the MGP model in the case of complete interaction graphs: it is equal to the class of graph languages decidable by a nondeterministic Turing Machine of linear space that receives its input graph by its adjacency matrix representation.