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There exists a total computable predicate P such that for any algorithm computing P(x) with running time T(x), there exists another algorithm computing P(x) with computation ...

A wavelet used in multiresolution representation to analyze the information content of images. The wavelet is defined by ...

For every infinite loop space machine E, there is a natural equivalence of spectra between EX and Segal's spectrum BX.

In most computer programs and computing environments, the precision of any calculation (even including addition) is limited by the word size of the computer, that is, by ...

The Church-Rosser theorem states that lambda calculus as a reduction system with lambda conversion rules satisfies the Church-Rosser property.

Church proved several important theorems that now go by the name Church's theorem. One of Church's theorems states that there is no consistent decidable extension of Peano ...

Computation time (also called "running time") is the length of time required to perform a computational process. Representation a computation as a sequence of rule ...

Given a sequence of independent random variates X_1, X_2, ..., if sigma_k^2=var(X_k) and rho_n^2=max_(k<=n)((sigma_k^2)/(s_n^2)), then lim_(n->infty)rho_n^2=0. This means ...

If the random variates X_1, X_2, ... satisfy the Lindeberg condition, then for all a<b, lim_(n->infty)P(a<(S_n)/(s_n)<b)=Phi(b)-Phi(a), where Phi is the normal distribution ...

Almost all processes that are not obviously simple can be viewed as computations of equivalent sophistication (Wolfram 2002, pp. 5 and 716-717). More specifically, the ...