# What is 3-SAT problem explain with example?

## What is 3-SAT problem explain with example?

Another variant is the not-all-equal 3-satisfiability problem (also called NAE3SAT). Given a conjunctive normal form with three literals per clause, the problem is to determine if an assignment to the variables exists such that in no clause all three literals have the same truth value.

### Is 3-SAT reducible to 2 SAT?

It is known that 3-SAT belong to – NP-Complete complexity problems, while 2-SAT belong to P as there is known polynomial solution to it. So you can state that there is no such reduction from 3-SAT to 2-SAT unless P=NP.

#### Is 3-SAT an NP?

Theorem : 3SAT is NP-complete. Proof : Evidently 3SAT is in NP, since SAT is in NP. To determine whether a boolean expression E in CNF is satisfiable, nondeterministically guess values for all the variables and then evaluate the expression. This can be carried out in nondeterministic polynomial time.

Does 3-SAT reduce to 4 SAT?

Input to 3-SAT can be converted into input to EXACT-4-SAT in polynomial time. If clause length is 2, we can use 2 new variables and replace the clause by 4 new clauses.

Is there a way to reduce clique to sat?

Here is one possible way to reduce Clique to SAT (you can then further reduce it to 3SAT). This type of reduction is often used in (propositional) proof complexity, an area of complexity theory.

## How to reduce a clique to a 3sat circuit?

If you want to reduce Clique directly to 3SAT, you can design a boolean circuit, where the input is a graph and a subset of vertices, and the output is TRUE if that subset is a clique and FALSE otherwise. If the graph has N vertices, you need: N variables, one for each vertex, which is TRUE if it is part of the subset and FALSE otherwise.

### Which is simpler the 2 SAT or the 3 SAT problem?

3-SAT defines the problem of determining whether a given CNF, with each clause containing at most literals, is satisfiable or not. The 3-SAT problem is simpler then 2-SAT as it seeks to solve the 2-SAT problem where there can be at most three variables in each parenthesis in the boolean expression.

#### How is the clique problem different from the independent set problem?

However, the two problems have different properties when applied to restricted families of graphs. For instance, the clique problem may be solved in polynomial time for planar graphs while the independent set problem remains NP-hard on planar graphs.