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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.
Since Lady Gaga's "Bad Romance" in 2009, every video that has reached the top of the "most-viewed YouTube videos" list has been a music video. In November 2005, a Nike advertisement featuring Brazilian football player Ronaldinho became the first video to reach 1,000,000 views. [1] The billion-view mark was first passed by Gangnam Style in ...
Go to Heaven is the eleventh studio album (sixteenth overall) by rock band the Grateful Dead, released April 28, 1980, by Arista Records. It is the band's first album with keyboardist Brent Mydland .
It runs in polynomial time on inputs that are in SUBSET-SUM if and only if P = NP: // Algorithm that accepts the NP-complete language SUBSET-SUM. // // this is a polynomial-time algorithm if and only if P = NP. // // "Polynomial-time" means it returns "yes" in polynomial time when // the answer should be "yes", and runs forever when it is "no".
M runs for polynomial time on all inputs; For all x in L, M outputs 1 with probability no less than 1/2; For all x not in L, M outputs 1 with probability strictly less than 1/2. Alternatively, PP can be defined using only deterministic Turing machines. A language L is in PP if and only if there exists a polynomial p and deterministic Turing ...
The music video for "Heaven" was directed by Luke Gilford and released on 19 January 2017. [5] According to a representative, Sivan was going to release the video on 20 January, to coincide with Donald Trump's inauguration. However, the release was forward a day due to an overwhelming response from fans to teasers for the clip. [6]
The song produced two music videos, the first one featuring women posed as various Renaissance era paintings. The second one features more John Legend himself and less posture women. Both videos were shot at Highclere Castle and directed by Hype Williams. The instrumental would be reused on "HEAVEN TO ME" (2023) by Tyler, The Creator.
An alternative characterization of PSPACE is the set of problems decidable by an alternating Turing machine in polynomial time, sometimes called APTIME or just AP. [4]A logical characterization of PSPACE from descriptive complexity theory is that it is the set of problems expressible in second-order logic with the addition of a transitive closure operator.