Is NP equal to Exptime?

Is NP equal to Exptime?

Relationships to other classes It is also known that if P = NP, then EXPTIME = NEXPTIME, the class of problems solvable in exponential time by a nondeterministic Turing machine.

Is P Poly in NP?

One of the most interesting reasons that P/poly is important is the property that if NP is not a subset of P/poly, then P ≠ NP. Although not all languages in P/poly are sparse languages, there is a polynomial-time Turing reduction from any language in P/poly to a sparse language.

Is NP a strict subset of EXPTIME?

It is known that P ⊆ NP ⊆ PSPACE ⊆ EXPTIME. EXPTIME = P. (Or in other words, P is a strict subset of EXPTIME, denoted as P ⊂ EXPTIME.) In complexity and cryptography PSPACE is considered efficient space, P is considered efficient time.

What is an example of an EXPSPACE complete problem?

An example of an EXPSPACE-complete problem is the problem of recognizing whether two regular expressions represent different languages, where the expressions are limited to four operators: union, concatenation, the Kleene star (zero or more copies of an expression), and squaring (two copies of an expression).

How do the hierarchy theorems apply to PSPACE vs exp?

The hierarchy theorems only let you compare like with like (e.g., they show that PSPACE ⊊ EXPSPACE and P ⊊ EXP) so they don’t directly apply to PSPACE vs EXP but they do give us a strong intuition that more resource means that more problems become solvable. A machine running in exponential time could use exponential space.

What is the difference between PSPACE and exp?

That’s what the difference is: although both PSPACE and EXP are problems that can be solved in exponential time, PSPACE is restricted to polynomial space use, whereas EXP can use exponential space. That already suggests that EXP ought to be more powerful. For example, suppose you’re trying to solve a problem about graphs.

Is extexpspace a strict superset of PSPACE?

EXPSPACE is known to be a strict superset of PSPACE, NP, and P. It is further suspected to be a strict superset of EXPTIME, however this is not known. ^ Meyer, A.R. and L. Stockmeyer.