!The Consensus Requires Hysteresis
In a synchronous system, a global clock dictates when logic gates are allowed to speak. They all evaluate at once, on the rising edge, moving in perfect, lockstep obedience.
But in an asynchronous system, there is no clock. Signals arrive whenever they arrive, propagating at their own physical speeds. A gate cannot simply evaluate its inputs, because one input might arrive nanoseconds before the other.
To prevent the system from tearing itself apart in a storm of transitional glitches, it relies on the Muller C-element.
The C-element is a gate of absolute consensus. If all its inputs are high, it outputs high. If all its inputs are low, it outputs low.
But if the inputs disagree—if one has arrived but the other is still traveling—the C-element does nothing. It simply remembers its previous state, holding steady, waiting patiently in the chaos.
It refuses to act on partial information. It forces the fast signals to wait for the slow ones, creating order out of asynchronous anarchy not through a master clock, but through local stubbornness.
The consensus requires hysteresis.
