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A Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean constants True/False or Yes/No, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions. [1] Boolean expressions correspond to propositional formulas in logic and are a special case of Boolean circuits. [2]
This step results in even numbers if the doubled value is less than or equal to N, and odd numbers if the doubled value is greater than N. For example, in Decimal applications where N is 10, original values between 0 and 4 result in even numbers and original values between 5 and 9 result in odd numbers, effectively re-packing the doubled values ...
Freivalds' algorithm (named after Rūsiņš Mārtiņš Freivalds) is a probabilistic randomized algorithm used to verify matrix multiplication.Given three n × n matrices, , and , a general problem is to verify whether =.
They return a negative number when the first argument is lexicographically smaller than the second, zero when the arguments are equal, and a positive number otherwise. This convention of returning the "sign of the difference" is extended to arbitrary comparison functions by the standard sorting function qsort , which takes a comparison function ...
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [ 1 ] [ 2 ] Alternative names are switching function , used especially in older computer science literature, [ 3 ] [ 4 ] and truth function (or logical function) , used in logic .
Similarly, a Boolean function of degree at most depends on at most coordinates, making it a junta (a function depending on a constant number of coordinates), where is an absolute constant equal to at least 1.5, and at most 4.41, as shown by Wellens. [5]
This algorithm results in the shortest possible superpermutation for all n less than or equal to 5, but becomes increasingly longer than the shortest possible as n increase beyond that. [ 2 ] Another way of finding superpermutations lies in creating a graph where each permutation is a vertex and every permutation is connected by an edge.
Majority function: their value is 1 on input vectors with more than n/2 ones; Threshold functions: their value is 1 on input vectors with k or more ones for a fixed k; All-equal and not-all-equal function: their values is 1 when the inputs do (not) all have the same value; Exact-count functions: their value is 1 on input vectors with k ones for ...