In computational complexity theory, the complexity class ⊕P (pronounced "parity P") is the class of decision problems solvable by a nondeterministic Turing machine in polynomial time, where the acceptance condition is that the number of accepting computation paths is odd. An example of a ⊕P problem is "does a given graph have an odd number of perfect matchings?" The class was defined by Papadimitriou and Zachos in 1983. ⊕P is a counting class, and can be seen as finding the least significant bit of the answer to the corresponding #P problem. The problem of finding the most significant bit is in PP. PP is believed to be a considerably harder class than ⊕P; for example, there is a relativized universe (see oracle machine) where P = ⊕P ≠ NP = PP = EXPTIME, as shown by Beigel, Buhrman, and Fortnow in 1998. While Toda's theorem shows that PPP contains PH, P⊕P is not known to even contain NP. However, the first part of the proof of Toda's theorem shows that BPP⊕P contains PH. Lance Fortnow has written a concise proof of this theorem. ⊕P contains the graph isomorphism problem, and in fact this problem is low for ⊕P. It also trivially contains UP, since all problems in UP have either zero or one accepting paths. More generally, ⊕P is low for itself, meaning that such a machine gains no power from being able to solve any ⊕P problem instantly. The ⊕ symbol in the name of the class may be a reference to use of the symbol ⊕ in Boolean algebra to refer the exclusive disjunction operator. This makes sense because if we consider "accepts" to be 1 and "not accepts" to be 0, the result of the machine is the exclusive disjunction of the results of each computation path. (Wikipedia).
Parity check is a simple method of checking for errors in a communications systems. I'm Mr. Woo and my channel is all about learning - I love doing it, and I love helping others to do it too. I guess that's why I became a teacher! I hope you get something out of these videos - I upload al
From playlist Communications & Network Systems
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From playlist Networking
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Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Using a Pareto Chart Example
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Check out the article on Pareto Analysis and download the Excel file here: https://magnimetrics.com/pareto-principle-in-financial-analysis/ Fill our survey for a FREE Benchmark Analysis template! https://forms.gle/A4MLhr7J5rRG1JBi8 If you like this video, drop a comment, give it a thumbs
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This video defines a parametric equations and shows how to graph a parametric equation by hand. http://mathispower4u.yolasite.com/
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In this series of physics lectures, Professor J.J. Binney explains how probabilities are obtained from quantum amplitudes, why they give rise to quantum interference, the concept of a complete set of amplitudes and how this defines a "quantum state". Notes and problem sets here http://www
From playlist James Binney - 2nd Year Quantum Mechanics
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From playlist James Binney - 2nd Year Quantum Mechanics
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MIT 6.02 Introduction to EECS II: Digital Communication Systems, Fall 2012 View the complete course: http://ocw.mit.edu/6-02F12 Instructor: George Verghese This lecture starts with historical applications of error control and convolutional codes in space programs. Convolutional codes are
From playlist MIT 6.02 Introduction to EECS II: Digital Communication Systems, Fall 2012
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From playlist Mathematics
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Strong Average-Case Circuit Lower Bounds from Non-trivial Derandomization - Lijie Chen
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