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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 .
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]
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).
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]
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-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted as logical values, for example, 0 = false and 1 = true, i.e., a single bit of information.
[1] [2] Indeed, a Boolean variable may be regarded (and implemented) as a numerical variable with one binary digit , or as a bit string of length one, which can store only two values. The implementation of Booleans in computers are most likely represented as a full word , rather than a bit; this is usually due to the ways computers transfer ...