On the Delay-Sensitivity of Gate Networks

In classical switching theory it is usually assumed that asynchronous sequential circuits are operated in the fundamental mode. In this mode, a circuit is started in a stable state; then the inputs are changed to cause a transition to another stable state. The inputs are not allowed to change again until the entire circuit has stabilized. In contrast to this, delay-insensitive circuits -the correctness of which is insensitive to delays in their components and wiresuse the input-output mode. Here, it is assumed that inputs may change again, in response to an output change, even before the entire circuit has stabilized. In this paper, we show that such commonly used behaviors as those of the set-reset latch and Muller's C-ELEMENT do not have delay-insensitive realizations, if gates are used as the basic components. In fact, we prove that no nontrivial sequential behavior with one binary input possesses a delay-insensitive realization using gates only. Our proof makes use of the equivalence between ternary simulation and the General Multiple Winner model of circuit behavior.