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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 .
In mathematics and mathematical logic, Boolean algebra is a branch of algebra.It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.
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]
An important set of problems in computational complexity involves finding assignments to the variables of a Boolean formula expressed in conjunctive normal form, such that the formula is true. The k -SAT problem is the problem of finding a satisfying assignment to a Boolean formula expressed in CNF in which each disjunction contains at most k ...
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. [2] There are 2 n+1 symmetric n-ary Boolean functions.
Boolean function with two different minimal forms. The Blake canonical form is the sum of the two. In Boolean logic , a formula for a Boolean function f is in Blake canonical form ( BCF ), [ 1 ] also called the complete sum of prime implicants , [ 2 ] the complete sum , [ 3 ] or the disjunctive prime form , [ 4 ] when it is a disjunction of all ...
The Boolean domain {0, 1} can be replaced by the unit interval [0,1], in which case rather than only taking values 0 or 1, any value between and including 0 and 1 can be assumed.
Boole's expansion theorem, often referred to as the Shannon expansion or decomposition, is the identity: = + ′ ′, where is any Boolean function, is a variable, ′ is the complement of , and and ′ are with the argument set equal to and to respectively.