How to prove Satisfiability of boolean formulas is NP-complete

  • Thread starter XodoX
  • Start date
  • Tags
    Formulas
In summary, proving the satisfiability of boolean formulas is NP-complete can be done using the Cook-Levin theorem, which states that any problem in NP can be reduced to the satisfiability problem. This means that if a solution to the satisfiability problem can be found, then it can be used to solve any problem in NP, making it NP-complete.
  • #1
XodoX
203
0
How to prove "Satisfiability of boolean formulas is NP-complete"

I can not figure out how to prove this. I have been trying to find something that explains it step by step, possibly even with an example. I can not find anything. Can somebody perhaps explain how you prove it or show me where I can find a thorough explanation ?
 
Physics news on Phys.org
  • #2


XodoX said:
I can not figure out how to prove this. I have been trying to find something that explains it step by step, possibly even with an example. I can not find anything. Can somebody perhaps explain how you prove it or show me where I can find a thorough explanation ?

Maybe this is what you are looking for:

http://en.wikipedia.org/wiki/Cook–Levin_theorem
 

1. What is the definition of NP-complete?

NP-complete is a term used in computational complexity theory to describe a class of problems that are believed to be the most difficult to solve among all problems in the complexity class NP (non-deterministic polynomial time). These problems have the property that if any one of them can be solved in polynomial time, then all other problems in NP can also be solved in polynomial time.

2. What does it mean for a problem to be NP-complete?

A problem is considered NP-complete if it belongs to the class NP and every other problem in NP can be reduced to it in polynomial time. This means that if a solution to an NP-complete problem can be found in polynomial time, then it can be used to solve any other NP problem in polynomial time as well.

3. How is the satisfiability of boolean formulas related to NP-complete?

The satisfiability of boolean formulas is a classic NP-complete problem. This means that it is one of the most difficult problems in the class NP, and if a polynomial-time algorithm for solving it is discovered, it would also mean that every other problem in NP can be solved in polynomial time.

4. How do you prove that satisfiability of boolean formulas is NP-complete?

To prove that a problem is NP-complete, you must show two things: 1) that it belongs to the class NP, and 2) that every other problem in NP can be reduced to it in polynomial time. This can be done by providing a polynomial-time reduction from a known NP-complete problem to the problem of satisfiability of boolean formulas.

5. Why is proving the NP-completeness of a problem important?

Proving NP-completeness of a problem is important because it allows us to better understand the complexity of the problem and its relationship to other problems. It also helps us identify which problems are likely to be the most difficult to solve, and can guide the development of more efficient algorithms and approaches for solving these problems.

Similar threads

Comp Sci Proving a Logic Rule with Boolean Algebra: Step-by-Step Guide
    • Engineering and Comp Sci Homework Help
Replies
15
Views
1K
Comp Sci Boolean simplification of a larger term?
    • Engineering and Comp Sci Homework Help
Replies
5
Views
1K
Proof of NP-completeness via reduction
    • Engineering and Comp Sci Homework Help
Replies
1
Views
975
Using Euler's formula to prove trig identities using "sum to product" technique
    • Calculus and Beyond Homework Help
Replies
4
Views
929
Cook's theorem breaks down under some oracle A
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
How to Design a Boolean Function for a Full Adder?
    • Engineering and Comp Sci Homework Help
Replies
11
Views
2K
Graph Contractability: NP-Complete or Not?
    • Engineering and Comp Sci Homework Help
Replies
4
Views
2K
Protein Folding and NP-Completeness
    • Programming and Computer Science
Replies
5
Views
2K
MHB How to Derive Answers Using N Formula
    • General Math
Replies
4
Views
864
I Are electrons universal problem solvers?
    • Quantum Physics
Replies
4
Views
732

Hot Threads

Recent Insights

Back
Top