The recognition and identification of symmetric switching functions

IN the design of switching circuits based on relay-contact networks, it is known that if the function which describes the network is of the symmetric type it leads to a network which is much more economical of switching elements than the best series-parallel circuit. C. E. Shannon1 first described this type of function and its associated relay contact network in 1938. His definition of the symmetric function was general, but most of the generality of concept has been lost in subsequent treatment of the subject. For example, S. H. Washburn2 defines the symmetric relay-contact network as ¿one in which the conditions for closing a particular input-to-output path are given & in terms of the number of relays operated and un-operated.¿ This particular type of network is derived from a restricted class of symmetric functions ¿ a class of functions which may be realized by means of iterative networks.3 There is a much larger class of symmetric functions contained within Shannon´s definition, and these can be realized only by means of non-iterative networks.