Cook–Levin theorem

Target entity: Cook–Levin theorem
Context triple: [P, NP, and NP-Completeness: The Basics of Complexity Theory, mainTopic, Cook–Levin theorem]

• A. Valiant–Vazirani theorem
  The Valiant–Vazirani theorem is a fundamental result in computational complexity theory showing that solving unique solutions of NP problems is, under randomized reductions, as hard as solving general NP problems, with major implications for the study of randomness and hardness of approximation.
• B. PCP theorem
  The PCP theorem is a fundamental result in computational complexity theory stating that every problem in NP has probabilistically checkable proofs that can be verified by examining only a constant number of bits, with major implications for the hardness of approximation.
• C. P versus NP problem
  The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
• D. Entscheidungsproblem
  The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
• E. Håstad’s switching lemma
  Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Cook–Levin theorem
Target entity description: The Cook–Levin theorem is a foundational result in computational complexity theory that established the Boolean satisfiability problem (SAT) as the first NP-complete problem, launching the theory of NP-completeness.

• A. Valiant–Vazirani theorem
  The Valiant–Vazirani theorem is a fundamental result in computational complexity theory showing that solving unique solutions of NP problems is, under randomized reductions, as hard as solving general NP problems, with major implications for the study of randomness and hardness of approximation.
• B. PCP theorem
  The PCP theorem is a fundamental result in computational complexity theory stating that every problem in NP has probabilistically checkable proofs that can be verified by examining only a constant number of bits, with major implications for the hardness of approximation.
• C. P versus NP problem
  The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
• D. Entscheidungsproblem
  The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
• E. Håstad’s switching lemma
  Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
• F. None of above. chosen