The closed semiring is an algebraic structure which unifies a family of path problems, including all-pairs shortest path, transitive closure and minimum spanning tree, defined on directed or undirected graphs. In resemblance to the dynamic programming formulation on closed semirings, we define a connectionist network architecture, called the binary relation inference network, to solve the problems represented. The extension and summary operators of closed semiring correspond to the site and unit functions of the network. But the network structure offers an obvious advantage of being simply extended for asynchronous and continuous-time operation. Analog circuits for the network are presented and simulation results are described, with particular reference to the minimum spanning tree problem.
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