Algorithms Analysis Practice Test 2025 – All-in-One Mastery Guide to Exam Success

The assertion that Circuit Satisfiability is NP-complete is indeed accurate due to the implications of the Cook-Levin Theorem. This theorem, established by Stephen Cook in 1971, was foundational in the field of computational complexity. It states that any problem in the class NP can be reduced to the Boolean satisfiability problem (SAT) in polynomial time.

Circuit Satisfiability, which specifically refers to the problem of determining if there exists an assignment of binary values to the inputs of a Boolean circuit such that the output is true, can be transformed into an instance of SAT. Because SAT is NP-complete and Circuit Satisfiability can be polynomially reduced to SAT, it follows that Circuit Satisfiability is also NP-complete.

This categorization of Circuit Satisfiability as NP-complete highlights its complexity and the fundamental role it plays in the broader landscape of NP problems. In essence, the Cook-Levin Theorem not only establishes SAT as NP-complete but also extends to problems like Circuit Satisfiability, affirming their status within the NP-complete classification.