# Is NP-complete in PSPACE?

## Is NP-complete in PSPACE?

We shall prove the existence of a problem in NP and PSPACE-complete. Since, PSPACE is closed under reductions and NP is contained in PSPACE, then we have that NP = PSPACE. The P versus NP problem is a major unsolved problem in computer science. This problem was introduced in 1971 by Stephen Cook .

## Is PSPACE harder than NP?

though you shouldn’t necessarily expect it to be as effective as SAT solvers have been for NP-complete problems, given that PSPACE-complete problems are believed to be harder than NP-complete problems.

What is the relationship between NP and PSPACE?

An equivalent definition of NP is the set of problems for which a solution can be verified in polynomial time. Examples will come soon. PSPACE is the set of problems that can be solved using polynomial space.

What is PSPACE-complete problem?

In computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input length (polynomial space) and if every other problem that can be solved in polynomial space can be transformed to it in polynomial time.

### Is PSPACE equal to NP?

Formal definition Because of Savitch’s theorem, NPSPACE is equivalent to PSPACE, essentially because a deterministic Turing machine can simulate a non-deterministic Turing machine without needing much more space (even though it may use much more time).

### Is sat in PSPACE?

SAT is in PSPACE Think of a truth-value assignment as a sequence of 0’s and 1’s, where 0 indicates false and 1 indicates true. If there are v variables, then there are v bits in the sequence.

Is NP-hard harder than NP-complete?

The set of NP-hard problems is a superset of the set of NP-complete problems. There are complexity classes more “difficult” than NP, for example PSPACE, EXPTIME or EXPSPACE, and all these contain NP-hard but not NP-complete problems. Turing halting problem is undecidable and it belongs to NP-Hard set.

Why is NPSPACE and PSPACE the same thing?

Because of Savitch’s theorem, NPSPACE is equivalent to PSPACE, essentially because a deterministic Turing machine can simulate a non-deterministic Turing machine without needing much more space (even though it may use much more time). Also, the complements of all problems in PSPACE are also in PSPACE, meaning that co-PSPACE = PSPACE.

#### Which is an example of a PSPACE complete problem?

An example of a PSPACE-complete problem is the quantified Boolean formula problem (usually abbreviated to QBF or TQBF; the T stands for “true”). ^ Rahul Jain; Zhengfeng Ji; Sarvagya Upadhyay; John Watrous (July 2009).

#### Are there any relations between PSPACE and NL?

The following relations are known between PSPACE and the complexity classes NL, P, NP, PH, EXPTIME and EXPSPACE (note that ⊊, meaning strict containment, is not the same as ⊈): From the third line, it follows that both in the first and in the second line, at least one of the set containments must be strict, but it is not known which.

Which is the archetypal PSPACE complete formula problem?

Quantified Boolean formulas. Nowadays, the archetypal PSPACE-complete problem is generally taken to be the quantified Boolean formula problem (usually abbreviated to QBF or TQBF; the T stands for “true”), a generalization of the first known NP-complete problem, the Boolean satisfiability problem (SAT).