Although Arbiter circuits never grant more than one request at a time, there is no way to build an Arbiter that will always reach a decision within a fixed time limit. Present-day Arbiters reach decisions very quickly on average, usually within about a few hundred picoseconds. (A picosecond is a trillionth of a second.) When faced with close calls, however, the circuits may occasionally take twice as long, and in very rare cases the time needed to make a decision may be 10 times as long as normal.

The fundamental difficulty in making these decisions is nicely illustrated by the parable of Buridan's ass. Attributed to Buridan, a 14th-century French philosopher, this parable suggests that an ass placed exactly between two equal piles of hay might starve to death because it would be unable to choose which pile to eat. Similar minor dilemmas are familiar in everyday life. For example, two people approaching a doorway at the same time may pause before deciding who will go through first. They can go through in either order, and Buridan's ass can eat from either pile of hay. In both cases, all that is needed is a way to break the tie.

An Arbiter breaks ties. Like a flip-flop circuit, an Arbiter has two stable states corresponding to the two choices. One can think of these states as the Pacific Ocean and the Gulf of Mexico. Each request to an Arbiter pushes the circuit toward one stable state or the other, just as a hailstone that falls in the Rocky Mountains can roll downhill toward the Pacific or the Gulf. Between the two stable states, however, there must be a meta-stable line, which is equivalent to the Continental Divide. If a hailstone falls precisely on the divide, it may balance momentarily on that sharp mountain ridge before tipping toward the Pacific or the Gulf. Similarly, if two requests arrive at an Arbiter within a few picoseconds of each other, the circuit may pause in its meta-stable state before reaching one of its stable states to break the tie.

   
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