Elementary analytic functions in VTC^0

06/24/2022

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by   Emil Jeřábek, et al.

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It is known that rational approximations of elementary analytic functions (exp, log, trigonometric, and hyperbolic functions, and their inverse functions) are computable in the weak complexity class TC^0. We show how to formalize the construction and basic properties of these functions in the corresponding theory of bounded arithmetic, 𝑉𝑇𝐶^0.