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In mathematics, a symmetric Boolean function is a Boolean function whose value does not depend on the permutation of its input bits, i.e., it depends only on the number of ones in the input.^{[1]}
The definition implies that instead of the truth table, traditionally used to represent Boolean functions, one may use a more compact representation for an n-variable symmetric Boolean function: the (n + 1)-vector, whose i-th entry (i = 0, ..., n) is the value of the function on an input vector with i ones.
A number of special cases are recognized.^{[1]}
Logic, Set theory, Statistics, Number theory, Mathematical logic
Logic, Mathematics, Cryptography, Boolean domain, Computational complexity theory
Boolean function, If and only if, Circuit complexity, Boolean circuits, Axiom of choice
Logic, Mathematical logic, Set theory, Metalogic, Non-classical logic