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Consensus Problem with the Existence of an Adversary Nanomachine
A nanomachine is considered to be the basic functional unit in nanotechnology. The rapid evolution in nanotechnology has provided appropriate development in miniaturization and fabrication of nanomachines with simple sensing, computation, data storing, communication and action capability. Further capabilities and applications can be enabled if multiple nanomachines communicate to perform collaborative and synchronous functions in a distributed manner to form a nanonetwork. In this paper the consensus problem in diffusion based molecular communication is considered in a network of $n$ nanomachines. A nanomachine $node_c$ that can control and direct processes in the network is one of the $n$ nanomachines. The considered model is time slotted. An adversary nanomachine $node_A$ is located within the transmission range of the network, where $node_A$ aims to jam the communication among these $n$ nanomachines. The adversary nanomachine $node_A$ is assumed to follow Poisson probabilistic distribution in diffusing its jamming molecules. The $n$ nanomachines need to estimate the concentration of the jamming molecules, in order to improve the possibility of reaching consensus, taking into account the additional jamming molecules in the environment. Thus, during the first $k$ time slots, each nanomachine from $n$ senses (listens to) the jamming molecules diffused by $node_A$, and stores the sensed molecular concentration during each time slot in a vector of length $k$. Based on the stored molecular concentration in its vector, each nanomachine from $n$ attempts to estimate the average of diffused jamming units. After estimating this value, the processes to reach consensus start. Each nanomachine $n$ has an initial value, the initial values of all nanomachines are diffused to $node_c$. Then $node_c$ computes the average of all initial values. However, $node_c$ also needs to take into account the jamming molecules when it computes the average of initial values. Thus, same as nanomachines $n$, $nod_c$ is assumed to estimate the jamming molecular concentration during the first $k$ time slot. Then, $node_c$ diffuses the average of the initial values to the other nanomachines $n$.