Elementary analytic functions in \(\mathsf{VT}\mathsf{C}^0\)

DOI10.1016/j.apal.2023.103269OpenAlexW4353051304MaRDI QIDQ2700809

Emil Jeřábek

Publication date: 27 April 2023

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.12164

zbMATH Keywords

bounded arithmeticmodels of arithmeticthreshold circuitselementary analytic functions

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Complexity of proofs (03F20) Exponential and trigonometric functions (33B10)

Related Items (1)

Models of VTC0$\mathsf {VTC^0}$ as exponential integer parts

Uses Software

• DLMF

Cites Work

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• Parallel computation with threshold functions
• Efficient threshold circuits for power series
• Uniform constant-depth threshold circuits for division and iterated multiplication.
• Iterated multiplication in \(VTC^0\)
• The irrationality measure of \(\pi\) is at most 7.103205334137\dots
• Open induction in a bounded arithmetic for \(\mathrm{TC}^{0}\)
• Threshold circuits of bounded depth
• On uniformity within \(NC^ 1\)
• Logarithmic Depth Circuits for Algebraic Functions
• On Threshold Circuits and Polynomial Computation
• Theories for TC0 and Other Small Complexity Classes
• Notes on polynomially bounded arithmetic
• Valued Fields
• A simple proof that 𝜋 is irrational

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