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A solved Rubik's Revenge cube. The Rubik's Revenge (also known as the 4×4×4 Rubik's Cube) is a 4×4×4 version of the Rubik's Cube.It was released in 1981. Invented by Péter Sebestény, the cube was nearly called the Sebestény Cube until a somewhat last-minute decision changed the puzzle's name to attract fans of the original Rubik's Cube. [1]
The manipulations of the Rubik's Cube form the Rubik's Cube group. The Rubik's Cube group (,) represents the structure of the Rubik's Cube mechanical puzzle.Each element of the set corresponds to a cube move, which is the effect of any sequence of rotations of the cube's faces.
An algorithm defines a sequence of layer rotations to transform a given state to another (usually less scrambled) state. Usually an algorithm is expressed as a printable character sequence according to some move notation. An algorithm can be considered to be a "smart" move. All algorithms are moves, but few moves are considered to be algorithms.
As illustrated to the right, the fixed centers, middle edges and corners can be treated as equivalent to a 3×3×3 cube. As a result, once reduction is complete the parity errors sometimes seen on the 4×4×4 cannot occur on the 5×5×5, or any cube with an odd number of layers. [9] The Yau5 method is named after its proposer, Robert Yau.
Parity learning is a problem in machine learning. An algorithm that solves this problem must find a function ƒ, given some samples (x, ƒ(x)) and the assurance that ƒ computes the parity of bits at some fixed locations. The samples are generated using some distribution over the input.
The J, T, F, and R-perms are all valid substitutes for the A-perm, while the N, V and Y-perm can do the same job as the E-perm. Even fewer algorithms can be used to solve PLL (as few as two, such as the A-perm and U-perm) at the expense of having to repeat these algorithms to solve other cases, with additional "looks" to identify the next step. [8]
A parity game. Circular nodes belong to player 0, rectangular nodes belong to player 1. On the left side is the winning region of player 0, on the right side is the winning region of player 1. A parity game is played on a colored directed graph, where each node has been colored by a priority – one of (usually) finitely many natural numbers ...
Formally, a parity check matrix H of a linear code C is a generator matrix of the dual code, C ⊥. This means that a codeword c is in C if and only if the matrix-vector product Hc ⊤ = 0 (some authors [1] would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations. [2]