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Parity only depends on the number of ones and is therefore a symmetric Boolean function.. The n-variable parity function and its negation are the only Boolean functions for which all disjunctive normal forms have the maximal number of 2 n − 1 monomials of length n and all conjunctive normal forms have the maximal number of 2 n − 1 clauses of length n.
Parity learning is a problem in machine learning. An algorithm that solves this problem must find a function ƒ, given some samples (x, ƒ(x)) and the assurance that ƒ computes the parity of bits at some fixed locations. The samples are generated using some distribution over the input.
Self-concordant function; Semi-differentiability; Semilinear map; Set function; List of set identities and relations; Shear mapping; Shekel function; Signomial; Similarity invariance; Soboleva modified hyperbolic tangent; Softmax function; Softplus; Splitting lemma (functions) Squeeze theorem; Steiner's calculus problem; Strongly unimodal ...
Understanding and mapping relationships between function spaces has many applications in engineering and the sciences. In particular, one can cast the problem of solving partial differential equations as identifying a map between function spaces, such as from an initial condition to a time-evolved state. In other PDEs this map takes an input ...
An example of problem in NC 1 is the parity check on a bit string. [6] The problem consists in counting the number of 1s in a string made of 1 and 0. A simple solution consists in summing all the string's bits.
A parity plot is a scatterplot that compares a set of results from a computational model against benchmark data. Each point has coordinates ( x , y ), where x is a benchmark value and y is the corresponding value from the model.
This can lead to poor performance [34] when the features are individually useless, but are useful when combined (a pathological case is found when the class is a parity function of the features). Overall the algorithm is more efficient (in terms of the amount of data required) than the theoretically optimal max-dependency selection, yet ...
It is possible for a function to be neither odd nor even, and for the case f(x) = 0, to be both odd and even. [20] The Taylor series of an even function contains only terms whose exponent is an even number, and the Taylor series of an odd function contains only terms whose exponent is an odd number. [21]