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In mathematics, a symmetric Boolean function is a Boolean function whose value does not depend on the order of its input bits, i.e., it depends only on the number of ones (or zeros) in the input. [1] For this reason they are also known as Boolean counting functions .
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]
Church numerals 0, 1, 2, ... Church Booleans are the Church encoding of the Boolean ... The following predicate tests whether the first argument is less-than-or-equal ...
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 .
propositional logic, Boolean algebra: The statement is true if and only if A is false. A slash placed through another operator is the same as placed in front. The prime symbol is placed after the negated thing, e.g. ′ [2]
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]
The few systems that calculate the majority function on an even number of inputs are often biased towards "0" – they produce "0" when exactly half the inputs are 0 – for example, a 4-input majority gate has a 0 output only when two or more 0's appear at its inputs. [1] In a few systems, the tie can be broken randomly. [2]
In computer science, a relational operator is a programming language construct or operator that tests or defines some kind of relation between two entities.These include numerical equality (e.g., 5 = 5) and inequalities (e.g., 4 ≥ 3).