The 4s/3t Sum-Networks and Solvability

A directed acyclic Sum-Network network consisting of sources, intermediate nodes and terminals have been considered whose solvability depends explicitly upon the network topology. The solvability of various sum-network such as networks with- at most two sources, at most two terminals, three sources and three terminals, and two disjoint paths between source-terminal pairs have been discussed and vital results have been given in the literature so far. In This research paper, the solvability of the sum network with four sources and three terminals is discussed. The solvability is simply to mean that all terminals can compute the required sum of all source symbols with rate at least one. This paper also gives a vital theorem for the solvability of such sum networks. In this paper, the relation between the two way connectivity and necessary condition of any 4s/3t sum network is discussed in general.