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Full-Text Articles in Physical Sciences and Mathematics
On The Computability Of Primitive Recursive Functions By Feedforward Artificial Neural Networks, Vladimir A. Kulyukin
On The Computability Of Primitive Recursive Functions By Feedforward Artificial Neural Networks, Vladimir A. Kulyukin
Computer Science Faculty and Staff Publications
We show that, for a primitive recursive function h(x, t), where x is a n-tuple of natural numbers and t is a natural number, there exists a feedforward artificial neural network 𝔑(x, t), such that for any n-tuple of natural numbers z and a positive natural number m, the first m + 1 terms of the sequence {h(z, t)} are the same as the terms of the tuple (𝔑(z, 0), ... ,𝔑(z, m)).
On Correspondences Between Feedforward Artificial Neural Networks On Finite Memory Automata And Classes Of Primitive Recursive Functions, Vladimir A. Kulyukin
On Correspondences Between Feedforward Artificial Neural Networks On Finite Memory Automata And Classes Of Primitive Recursive Functions, Vladimir A. Kulyukin
Computer Science Faculty and Staff Publications
When realized on computational devices with finite quantities of memory, feedforward artificial neural networks and the functions they compute cease being abstract mathematical objects and turn into executable programs generating concrete computations. To differentiate between feedforward artificial neural networks and their functions as abstract mathematical objects and the realizations of these networks and functions on finite memory devices, we introduce the categories of general and actual computabilities and show that there exist correspondences, i.e., bijections, between functions computable by trained feedforward artificial neural networks on finite memory automata and classes of primitive recursive functions.