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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. Second, Boolean algebra uses logical operators such ...
The Boolean satisfiability problem (SAT) is, given a formula, to check whether it is satisfiable. This decision problem is of central importance in many areas of computer science, including theoretical computer science, complexity theory, [3][4] algorithmics, cryptography [5][6] and artificial intelligence. [7][additional citation (s) needed]
e. In logic, a functionally complete set of logical connectives or Boolean operators is one that can be used to express all possible truth tables by combining members of the set into a Boolean expression. [1][2] A well-known complete set of connectives is { AND, NOT }. Each of the singleton sets { NAND } and { NOR } is functionally complete.
A function problem consists of a partial function f; the informal "problem" is to compute the values of f on the inputs for which it is defined. Every function problem can be turned into a decision problem; the decision problem is just the graph of the associated function. (The graph of a function f is the set of pairs (x,y) such that f(x) = y ...
The halting problem is a decision problem about properties of computer programs on a fixed Turing-complete model of computation, i.e., all programs that can be written in some given programming language that is general enough to be equivalent to a Turing machine. The problem is to determine, given a program and an input to the program, whether ...
t. e. In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. [1] The set X is called the domain of the function [2] and the set Y is called the codomain of the function. [3] Functions were originally the idealization of how a varying quantity depends on another quantity.
The quadratic formula =. is a closed form of the solutions to the general quadratic equation + + =. More generally, in the context of polynomial equations, a closed form of a solution is a solution in radicals; that is, a closed-form expression for which the allowed functions are only n th-roots and field operations (+,,, /).
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1-p).