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In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize the classes NP and co-NP. [1] Each class in the hierarchy is contained within PSPACE. The hierarchy can be defined using oracle machines or alternating Turing machines.
The class P #P consists of all the problems that can be solved in polynomial time if you have access to instantaneous answers to any counting problem in #P (polynomial time relative to a #P oracle). Thus Toda's theorem implies that for any problem in the polynomial hierarchy there is a deterministic polynomial-time Turing reduction to a ...
If graph isomorphism is NP-complete, the polynomial time hierarchy collapses to its second level. [21] Since it is widely believed that the polynomial hierarchy does not collapse to any finite level, it is believed that graph isomorphism is not NP-complete. The best algorithm for this problem, due to László Babai, runs in quasi-polynomial ...
Pictorial representation of the polynomial time hierarchy. The arrows denote inclusion. In computational complexity theory of computer science, the structural complexity theory or simply structural complexity is the study of complexity classes, rather than computational complexity of individual problems and algorithms. It involves the research ...
For example, x²-6 is a polynomial with integer coefficients, since 1 and -6 are integers. The roots of x²-6=0 are x=√6 and x=-√6, so that means √6 and -√6 are algebraic numbers.
The union of the classes in the polynomial hierarchy: P NP: Solvable in polynomial time with an oracle for a problem in NP; also known as Δ 2 P PP: Probabilistically Polynomial (answer is right with probability slightly more than 1/2) PPAD: Polynomial Parity Arguments on Directed graphs PR: Solvable by recursively building up arithmetic ...
Football fans are getting ready for Super Bowl 59 as the Kansas City Chiefs go head-to-head against the Philadelphia Eagles at the Superdome in New Orleans, marking the second time in three years ...
The Fed held off on another rate cut at its Jan. 29 meeting. Here's what it means for your finances.