Lecture 29: Np-hard Problems [fa'13] 29 Np-hard Problems 29.1 a Game You Can't Win

A salesman in a red suit who looks suspiciously like Tom Waits presents you with a black steel box with n binary switches on the front and a light bulb on the top. The salesman tells you that the state of the light bulb is controlled by a complex boolean circuit—a collection of AND, OR, and NOT gates connected by wires, with one input wire for each switch and a single output wire for the light bulb. He then asks you the following question: Is there a way to set the switches so that the light bulb turns on? If you can answer this question correctly, he will give you the box and a billion dollars; if you answer incorrectly, or if you die without answering at all, he will take your soul.