Is BPP equal to P?

. As a result, P = NP leads to P = BPP since PH collapses to P in this case. Thus either P = BPP or P ≠ NP or both. Adleman’s theorem states that membership in any language in BPP can be determined by a family of polynomial-size Boolean circuits, which means BPP is contained in P/poly.

Is it possible for a problem to be in both P and NP?

Is it possible for a problem to be in both P and NP? Yes. Since P is a subset of NP, every problem in P is in both P and NP.

Is NL equal to Pspace?

NL can be formally defined in terms of the computational resource nondeterministic space (or NSPACE) as NL = NSPACE(log n). Important results in complexity theory allow us to relate this complexity class with other classes, telling us about the relative power of the resources involved.

What happens when NP equals P?

If P equals NP, every NP problem would contain a hidden shortcut, allowing computers to quickly find perfect solutions to them. But if P does not equal NP, then no such shortcuts exist, and computers’ problem-solving powers will remain fundamentally and permanently limited.

Is BPP a subset of RP?

Note that both RP and co-RP are subsets of BPP.

Is BPP closed under complement?

BPP and ZPP are both closed under complement.

Is NL a coNL?

Today we see the result that nondeterministic logspace, NL is closed under complement. The result was proved by Neil Immerman and Róbert Szelepcsényi in 1987. Theorem 1 NL = coNL. Towards this end, we show that the coNL-complete language is contained in NL.

Is P subset of PSPACE?

By Savitch’s Theorem, NPSPACE = PSPACE. Clearly, P subset PSPACE and NP subset NPSPACE, so P subset NP subset NPSPACE = PSPACE. What about coNP?

Does P equal NP?

Roughly speaking, P is a set of relatively easy problems, and NP is a set that includes what seem to be very, very hard problems, so P = NP would imply that the apparently hard problems actually have relatively easy solutions.

What is P not equal to NP?

The P versus NP problem is a major unsolved problem in computer science. If it turns out that P ≠ NP, which is widely believed, it would mean that there are problems in NP that are harder to compute than to verify: they could not be solved in polynomial time, but the answer could be verified in polynomial time.

What is computational complexity theory?

Computational complexity theory is a subfield of theoretical computer science one of whose primary goals is to classify and compare the practical difficulty of solving problems about finite combinatorial objects – e.g. given two natural numbers n and m, are they relatively prime?

What is computational theory in Computer Science?

The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage.

How does the theory of Computer Science formalize intuition?

The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used,…

What is computational problem and problem instance?

A computational problem can be viewed as an infinite collection of instances together with a solution for every instance. The input string for a computational problem is referred to as a problem instance, and should not be confused with the problem itself. In computational complexity theory, a problem refers to the abstract question to be solved.