Circuit-Satisfiability Problem

Given a boolean combination circuit composed of AND, OR, and NOT gates, is it satisfiable?

CIRCUIT-SAT = {$\langle$C$\rangle$$\mid$ C is a satisfiable boolean combinational circuit}

where $\langle$C$\rangle$ is a binary-string encoding of the circuit (e.g., as a graph)

Determining membership in CIRCUIT-SAT would require checking the 2^k possible binary assignments to the k inputs of a circuit.

There is strong evidence that CIRCUIT-SAT P.