Co-learning of total recursive functions

Let h be a recursive function. A partial recursive function ψ is i.o. (infinitely often) h-complex if every program for ψ requires more than h(χ) steps to compute ψ(χ) for infinitely many inputs χ. A more stringent notion is that of ψ being a.e. (almost ...

Recently, functions over the reals that extend elementarily computable functions over the integers have been proved to correspond to the smallest class of real functions containing some basic functions and closed by composition and linear integration.

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Suppose that n is even. Let $${\mathbb{F}_2}$$ denote the two-element field and $${\mathbb{Z}}$$ the set of integers. Bent functions can be defined as 1-valued functions on $${\mathbb{F}_2^n}$$ with 1-valued Fourier transform. More generally we call a mapping f on $${\mathbb{F}_2^n}$$ a $${\mathbb{Z}}$$ -bent function if both f and its ...