64 BELL SYSTEM TECHNICAL JOURNAL 



A hindrance function corresponds explicitly to a series-parallel type of 

 circuit, i.e. a circuit containing only series and parallel connections. This 

 is because the expression is made up of sum and product operations. There 

 is however, a hindrance function representing the operating characteristics 

 (conditions for open or closed circuits between the two terminals) for any 

 network, series-parallel or not. The hindrance for non-series-parallel net- 

 works can be found by several methods of which one is indicated in Fig. 5 

 for a simple bridge circuit. The hindrance is written as the product of a 

 set of factors. Each factor is the series hindrance of a possible path between 

 the two terminals. Further details concerning the Boolean method for 

 switching circuits may be found in the references cited above. 



This paper is concerned with the problem of synthesizing a two-terminal 

 circuit which represents a given hindrance function /(A^i , • • • , X„). Since 

 any given function / can be realized in an unlimited number of different 



f = (w+X)fZ+S)(W + Y + S)(Z+Y + X) 



Fig. 5 — Hindrance of a bridge circuit. 



ways, the particular design chosen must depend upon other considerations. 

 The most common of these determining criteria is that of economy of ele- 

 ments, which may be of several types, for example: 



(1) We may wish to realize our function with the least total number of 

 switching elements, regardless of which variables they represent. 



(2) We may wish to find the circuit using the least total number of relay 

 springs. This requirement sometimes leads to a solution different 

 from (1), since contiguous make and break elements may be combined 

 into transfer elements so that circuits which tend to group make and 

 break contacts on the same relay into pairs will be advantageous 

 for (2) but not necessarily for (1). 



(3) We may wish to distribute the spring loading on all the relays or on 

 some subset of the relays as evenly as possible. Thus, we might try 

 to find the circuit in which the most heavily loaded relay was as 

 lightly loaded as possible. More generally, we might desire a circuit 

 in which the loading on the relays is of some specified sort, or as near 

 as possible to this given distribution. For example, if the relay Xi 



