Abstract
The paper develops a strictly mathematical, unified theory of combinational switching networks, with the aid of linear graph theory and lattice algebra. The theory is based on the concept of a lattice-weighted, directed linear graph, termed switching net. The advantages of using lattice algebra, rather than Boolean algebra are emphasized. A calculus of lattice matrices is outlined in Section II, and then applied to the study of switching nets (Section III). A suitable formulation of Ashenhurst's uniqueness theorem, and a modified version of its proof are given in Section IV. In Section V switching net theory is extended to multi-terminal and reiterative nets, generalizing results due to M.L. Tsetlin and A.Sh. Blokh.
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