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Another form of logic puzzle, popular among puzzle enthusiasts and available in magazines dedicated to the subject, is a format in which the set-up to a scenario is given, as well as the object (for example, determine who brought what dog to a dog show, and what breed each dog was), certain clues are given ("neither Misty nor Rex is the German Shepherd"), and then the reader fills out a matrix ...
For the example below, there are four sides: A, B, C and the final result ABC. A is a 10×30 matrix, B is a 30×5 matrix, C is a 5×60 matrix, and the final result is a 10×60 matrix. The regular polygon for this example is a 4-gon, i.e. a square: The matrix product AB is a 10x5 matrix and BC is a 30x60 matrix.
In vector logic, the matrix-vector structure of logical operators is an exact translation to the format of linear algebra of these Boolean polynomials, where the x and 1−x correspond to vectors s and n respectively (the same for y and 1−y). In the example of NAND, f(1,1)=n and f(1,0)=f(0,1)=f(0,0)=s and the matrix version becomes:
A permutation matrix is a (0, 1)-matrix, all of whose columns and rows each have exactly one nonzero element.. A Costas array is a special case of a permutation matrix.; An incidence matrix in combinatorics and finite geometry has ones to indicate incidence between points (or vertices) and lines of a geometry, blocks of a block design, or edges of a graph.
Examples: 0 or 0 = 0; 0 or 1 = 1; 1 or 0 = 1; 1 or 1 = 1; 1010 or 1100 = 1110; The or operator can be used to set bits in a bit field to 1, by or-ing the field with a constant field with the relevant bits set to 1. For example, x = x | 0b00000001 will force the final bit to 1, while leaving other bits unchanged. [citation needed]
Another special case is the class of problems where each clause contains XOR (i.e. exclusive or) rather than (plain) OR operators. [e] This is in P, since an XOR-SAT formula can also be viewed as a system of linear equations mod 2, and can be solved in cubic time by Gaussian elimination; [18] see the box for an example.
Computing the position of a particular unique tuple or matrix in a de Bruijn sequence or torus is known as the de Bruijn decoding problem. Efficient O ( n log n ) {\displaystyle \color {Blue}O(n\log n)} decoding algorithms exist for special, recursively constructed sequences [ 17 ] and extend to the two-dimensional case.
In software engineering, a class diagram [1] in the Unified Modeling Language (UML) is a type of static structure diagram that describes the structure of a system by showing the system's classes, their attributes, operations (or methods), and the relationships among objects. The class diagram is the main building block of object-oriented modeling.