Computer Science Department
School of Computer Science, Carnegie Mellon University


On the Complexity of MAX/MIN/AVRG Circuits

Manuel Blum, Rache Rue, Ke Yang

March 2002

Keywords: Circuits, complexity, NP, co-NP, two-person game

We study the complexity of a class of circuits, namely, the MAX/MIN/AVRG circuits. On the wires of these circuits are real values between 0 and 1; the functions each gate performs are MAX, MIN, and AVERAGE of fan-in 2; there can be feed-backs in the circuit. It can be shown that every such circuit has at least a "stable" solution, meaning that there is a way to set each wire to a particular value such that each gate is satisfied. However, finding a stable solution in polynomial time seems to be a tricky problem and remains unsolved. We discuss some results concerning this computation model, as well as its applications.

31 pages

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