SYNTHESIS OF SWirCIIING CIRCUITS 



95 



other ones, since at least this many equahties exist between the functions to 

 be joined to these terminals. This will, in general, produce a considerable 

 reduction in the contact requirements on the remaining variables. Also an 

 economy can usually be achieved in the M network. In order to apply this 



INDEPENDENT 

 OF X.Y 



Fig. 22 — Networks for group invariance in two variables. 



Fig. 23 — Networks for group invariance in three variables. 



method of design, however, it is essential that we have a method of deter- 

 mining which, if any, of the iV, Sj leave a function unchanged. The 

 following theorem, although not all that might be hoped for, shows that we 

 don't need to evaluate NiSJior all NiSj but only the N if and Sjf. 



Theorem 14: A necessary and sufficient condition that NiSjf = f is that 

 N<f = SJ. 



This follows immediately from the self inverse property of the iV,-. Of 



