Chức năng này sẽ khó kiểm soát. Trong một tĩnh mạch tương tự, observability của một nút phụ thuộc vào các yếu tố mà qua đó các tín hiệu của nó phải tuyên truyền để đạt được một đầu ra. Observability của nó có thể không tốt hơn so với các observability của các yếu tố mà qua đó nó phải được định hướng. | CONTROLLABILITY OBSERVABILITY ANALYSIS 397 function will be difficult to control. In a similar vein the observability of a node depends on the elements through which its signals must propagate to reach an output. Its observability can be no better than the observability of the elements through which it must be driven. Therefore before applying the SCOAP algorithm to a circuit it is necessary to have for each primitive that appears in a circuit equations expressing the 0- and 1-controllability of its output in terms of the controllability of its inputs and it is necessary to have equations that express the observability of each input in terms of both the observability of that element and the controllability of some or all of its other inputs. Consider the three-input AND gate. To get a 1 on the output all three inputs must be set to 1. Hence controllability of the output to a 1 state is a function of the controllability of all three inputs. To produce a 0 on the output requires only that a single input be at 0 thus there are three choices and if there exists some quantitative measure indicating the relative ease or difficulty of controlling each of these three inputs then it is reasonable to select the input that is easiest to control in order to establish a 0 on the output. Therefore the combinational 1- and 0-controllabilities CCl Y and CC Y of a three-input AND gate with inputs X1 X2 and X3 and output Y can be defined as CC1 Y CC1 X1 CC1 X2 CC1 X3 1 CC0 Y Min CC0 X1 CC0 X2 CC0 X3 1 Controllability to 1 is additive over all inputs and to 0 it is the minimum over all inputs. In either case the result is incremented by 1 so that for intermediate nodes the number reflects at least in part distance measured in numbers of gates to primary inputs and outputs. The controllability equations for any combinational function can be determined from either its truth table or its cover. If two or more inputs must be controlled to 0 or 1 values in order to produce the value e e e
