Advanced Topic 38 of 51 Theory & Discrete Math
Cook-Levin Theorem
Result proving SAT is NP-complete.
How it works
Cook and Levin proved SAT is NP-complete by encoding a nondeterministic TM's computation as a Boolean formula in polynomial size. Reductions from SAT then prove other problems NP-complete.
Where it is used
The first NP-complete problem.
Common pitfall
It is the basis of all later NP-completeness proofs.
Where it fits in the course
Cook-Levin Theorem is topic 38 of 51 in Theory & Discrete Math, rated Advanced. It follows NP-Completeness. The next topic is P vs NP.
Practice and explore
- Open the interactive lesson, with a mini quiz.
- Take the Theory & Discrete Math quiz.
How to study this topic
- Read the explanation above and restate the definition in your own words.
- Open the interactive lesson and answer its mini quiz.
- Read the common pitfall, then write a short example that avoids it.
- Check your understanding in the Theory & Discrete Math quiz, and revisit the topic if you miss a question.
Frequently asked questions
What is Cook-Levin Theorem?
Result proving SAT is NP-complete. It belongs to Theory & Discrete Math and is an advanced-level topic.
Where do people use Cook-Levin Theorem?
The first NP-complete problem.
What is the most common mistake with Cook-Levin Theorem?
It is the basis of all later NP-completeness proofs.
What should I learn before this topic?
Start with NP-Completeness, the topic just before it in Theory & Discrete Math.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Theory & Discrete Math quiz.
Is Cook-Levin Theorem hard to learn?
It is an Advanced topic. Expect to read the explanation more than once and to connect it with earlier topics. Working through a small example by hand helps most.
How long does it take to learn Cook-Levin Theorem?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Cook-Levin Theorem?
NP-Completeness, P vs NP, Class NP are closely connected. The full list is in the related topics section of this page.
What should I study after Cook-Levin Theorem?
Continue with P vs NP, the next topic in Theory & Discrete Math.
Related topics
- NP-Completeness (Theory & Discrete Math)
- P vs NP (Theory & Discrete Math)
- Class NP (Theory & Discrete Math)
- SAT Problem (Theory & Discrete Math)
- Bayes' Theorem (Math for Computing)
- Master Theorem (Algorithms)
- Central Limit Theorem (Math for Computing)