NP-Complete problems NP-Complete problems - Ace

✬✩SAT: Poly-time reductionThe reduction is as follows:• For each wire x i in the circuit C, the formula φ has avariable x i .• For each gate in C, make a formula involving the variablesof its incident wires that fully describes the behaviour of thegate.– For example, the operation of the output OR gate(figure on the next page) is x 5 ↔ (x 1 ∨x 2 ).• The formula φ produced by the reduction is the AND of thecircuit-output variable with the conjunction of clausesdescribing the operation of each gate.CS404/504✫Design and Analysis of Algorithms: Lecture 26Computer Science17✪