Abstract: In this paper, we propose simple protocols for enabling two communicating agents that may have never met before to extract common knowledge out of any initial knowledge that each of them possesses. The initial knowledge from which the agents start, may even be independent of each other, implying that the two agents need not have had previous access to common information sources. In addition, the common knowledge extracted upon the termination of the protocols depends, in a fair way, on the (possibly independent) information items initially known, separately, by the two agents. It is fair in the sense that there is a negotiation between the two agents instead of one agent forcing the other to conform to its own knowledge. These protocols, may be extended in order to support security applications where the establishment of a common knowledge is required. Moreover, the implementation of the protocols leads to reasonably small code that can also fit within resource limited devices involved in any communication network while, at the same time, it is efficient as simulation results demonstrate.

Abstract: In this work, we study the propagation of influence and computation in dynamic networks that are possibly disconnected at every instant. We focus on a synchronous message passing communication model with broadcast and bidirectional links. To allow for bounded end-to-end communication we propose a set of minimal temporal connectivity conditions that bound from the above the time it takes for information to make progress in the network. We show that even in dynamic networks that are disconnected at every instant information may spread as fast as in networks that are connected at every instant. Further, we investigate termination criteria when the nodes know some upper bound on each of the temporal connectivity conditions. We exploit our termination criteria to provide efficient protocols (optimal in some cases) that solve the fundamental counting and all-to-all token dissemination (or gossip) problems. Finally, we show that any protocol that is correct in instantaneous connectivity networks can be adapted to work in temporally connected networks.

Abstract: In this work, we study the propagation of influence and computation in dynamic distributed computing systems that are possibly disconnected at every instant. We focus on a synchronous message-passing communication model with broadcast and bidirectional links. Our network dynamicity assumption is a worst-case dynamicity controlled by an adversary scheduler, which has received much attention recently. We replace the usual (in worst-case dynamic networks) assumption that the network is connected at every instant by minimal temporal connectivity conditions. Our conditions only require that another causal influence occurs within every time window of some given length. Based on this basic idea, we define several novel metrics for capturing the speed of information spreading in a dynamic network. We present several results that correlate these metrics. Moreover, we investigate termination criteria in networks in which an upper bound on any of these metrics is known. We exploit our termination criteria to provide efficient (and optimal in some cases) protocols that solve the fundamental counting and all-to-all token dissemination (or gossip) problems.

Abstract: In this chapter, our focus is on computational network analysis from a theoretical point of view. In particular, we study the \emph{propagation of influence and computation in dynamic distributed computing systems}. We focus on a \emph{synchronous message passing} communication model with bidirectional links. Our network dynamicity assumption is a \emph{worst-case dynamicity} controlled by an adversary scheduler, which has received much attention recently. We first study the fundamental \emph{naming} and \emph{counting} problems (and some variations) in
networks that are \emph{anonymous}, \emph{unknown}, and possibly dynamic. Network dynamicity is modeled here by the \emph{1-interval connectivity model}, in which communication is synchronous and a (worst-case) adversary
chooses the edges of every round subject to the condition that each instance is connected. We then replace this quite strong assumption by minimal \emph{temporal connectivity} conditions. These conditions only require that \emph{another causal influence occurs within every time-window of some given length}. Based on this basic idea we define several novel metrics for capturing the speed of information spreading in a dynamic network. We present several results that correlate these metrics. Moreover, we investigate \emph{termination criteria} in networks in which an upper bound on any of these metrics is known. We exploit these termination criteria to provide efficient (and optimal in some cases) protocols that solve the fundamental \emph{counting} and \emph{all-to-all token dissemination} (or \emph{gossip}) problems. Finally, we propose another model of worst-case temporal connectivity, called \emph{local
communication windows}, that assumes a fixed underlying communication network and restricts the adversary to allow communication between local neighborhoods in every time-window of some fixed length. We prove some basic properties and provide a protocol for counting in this model.

Abstract: This paper addresses the problem of counting the size of a network where (i) processes have the same identifiers (anonymous nodes) and (ii) the et-
work topology constantly changes (dynamic network). Changes are riven by a powerful adversary that can look at internal process states and add and remove edges in order to contrast the convergence of the algorithm to the correct count. The paper proposes two leader-based counting algorithms. Such algorithms are based on a technique that mimics an energy-transfer between network nodes. The first algorithm assumes that the adversary cannot generate either disconnected network graphs or network graphs where nodes have degree greater than D. In such algorithm, the leader can count the size of the network and detect the counting termination in a finite time (i.e., conscious counting algorithm). The second algorithm assumes that the adversary only keeps the network graph connected at any time and we prove that the leader can still converge to a correct count in a finite number of rounds, but it is not conscious when this convergence happens.

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 extend the population protocol model with a cover-time service that informs a walking state every time it covers the whole network. This represents a known upper bound on the cover time of a random walk. The cover-time service allows us to introduce termination into population protocols, a capability that is crucial for any distributed system. By reduction to an oracle-model we arrive at a very satisfactory lower bound on the computational power of the model: we prove that it is at least as strong as a Turing Machine of space log n with input commutativity, where n is the number of nodes in the network. We also give a log n-space, but nondeterministic this time, upper bound. Finally, we prove interesting similarities of this model to linear bounded automata.

Abstract: We extend the population protocol model with a cover-time service that informs a walking state every time it covers the whole network. This is simply a known upper bound on the cover time of a random walk. This allows us to introduce termination into population protocols, a capability that is crucial for any distributed system. By reduction to an oracle-model we arrive at a very satisfactory lower bound on the computational power of the model: we prove that it is at least as strong as a Turing Machine of space logn with input commutativity, where n is the number of nodes in the network. We also give a logn-space, but nondeterministic this time, upper bound. Finally, we prove interesting similarities of this model to linear bounded automata.