Elementary analytic functions in $VTC^0$

Abstract

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 $\mathrm{TC}^0$. We show how to formalize the construction and basic properties of these functions in the corresponding theory of bounded arithmetic, $\mathsf{VTC}^0$.