Is PSPACE equal to EXPTIME?

Is PSPACE equal to EXPTIME?

This article shows that PSPACE not equal EXP. A simple but novel proof technique has been used to separate these two classes. Whether an arbitrary Turing machine accepts an input when the running time is limited has been computed in this paper.

What is relation between PSPACE and EXPTIME?

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.

Why is PSPACE in EXPTIME?

EXPTIME can be reformulated as the space class APSPACE, the set of all problems that can be solved by an alternating Turing machine in polynomial space. This is one way to see that PSPACE ⊆ EXPTIME, since an alternating Turing machine is at least as powerful as a deterministic Turing machine.

Is PSPACE a 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.

Is NP-hard in EXPTIME?

The two classes are incomparable: neither is a subset of the other. There are problems in EXPTIME that are not NP-hard. The languages ∅ and Σ∗ are both in EXPTIME but are definitely not NP-hard since no other language can be many-one reduced to either of them.

What is meant by NP-hard?

A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP- problem (nondeterministic polynomial time) problem. NP-hard therefore means “at least as hard as any NP-problem,” although it might, in fact, be harder.

Are NP-hard problems NP-complete?

A problem X is NP-Complete if there is an NP problem Y, such that Y is reducible to X in polynomial time. NP-Complete problems are as hard as NP problems….Difference between NP-Hard and NP-Complete:

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. This observation was the center of many attempts to prove P ≠ NP. It is known that for a random oracle A, NPA is not a subset of PA/poly with probability 1.

Is chess a NP?

For this reason games like chess cannot themselves be NP-complete, as they only have a finite (albeit unthinkably large) number of possible positions.

Why is SAT NP complete?

SAT is in NP because any assignment of Boolean values to Boolean variables that is claimed to satisfy the given expression can be verified in polynomial time by a deterministic Turing machine.

What is the difference between EXPTIME and 2-EXPTIME?

EXPTIME is one class in an exponential hierarchy of complexity classes with increasingly more complex oracles or quantifier alternations. The class 2-EXPTIME is defined similarly to EXPTIME but with a doubly exponential time bound . This can be generalized to higher and higher time bounds.

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.

What is the difference between NP and NEXPTIME?

Most experts believe all the inclusions are proper. It is also known that if P = NP, then EXPTIME = NEXPTIME, the class of problems solvable in exponential time by a nondeterministic Turing machine. More precisely, EXPTIME ≠ NEXPTIME if and only if there exist sparse languages in NP that are not in P.

What is the meaning of exp in Computer Science?

In computational complexity theory, the complexity class EXPTIME (sometimes called EXP or DEXPTIME) is the set of all decision problems that have exponential runtime, i.e., that are solvable by a deterministic Turing machine in O (2 p(n)) time, where p ( n) is a polynomial function of n .