N-Terminal Switching Circuits

In a recent issue of T h e Bell System Technical Journal 1 , C. E. S h a n n o n discussed the synthesis of two-terminal relay c o n t a c t n e t w o r k s . Some of his results will be generalized in this p a p e r to iY-terminal networks which use selector switches with a n y n u m b e r of positions instead of t h e two of a relay. T h e kind of circuit which will be considered m a y be visualized as a black box with N accessible terminals a n d with M s h a f t s extending f r o m it. E a c h s h a f t operates a selector switch (which will usually consist of several simple selector switches ganged together) inside t h e box. T h e rotors a n d cont a c t s inside the box are connected electrically to one a n o t h e r a n d to the N terminals so t h a t each w a y of setting the M s h a f t s determines a p a t t e r n of interconnection of the N terminals. We do not p e r m i t the black box to contain relay m a g n e t s or o t h e r devices which would allow the circuit to operate sequentially. Because of this restriction our results a p p l y only to the simplest kind of switching circuit in which t h e s t a t e of the IV terminals d e p e n d s only on the present s t a t e of the M shafts, a n d not on t h e p a s t history of the s h a f t s . We m a y t h e n use the t e r m N-terminal switching function to m e a n a rule which assigns to each w a y of setting the M s h a f t s a s t a t e of the terminals. We are concerned with t h e problem of synthesis: given an iV-terminal switching f u n c t i o n /, to find a switching circuit for which the s t a t e s of t h e s h a f t s a n d terminals correspond i n the w a y indicated b y / .