On the complexity of algebraic numbers, and the bit-complexity of straight-line programs1-Reference-Cited by-同舟云学术

On the complexity of algebraic numbers, and the bit-complexity of straight-line programs1

Published:2023-06-21 Issue:2 Volume:12 Page:145-173
ISSN:2211-3576
Container-title:Computability
language:
Short-container-title:COM

Author:

Allender Eric¹,Balaji Nikhil²,Datta Samir³,Pratap Rameshwar⁴

Affiliation:

1. Department of Computer Science, Rutgers University, NJ, USA

2. Indian Institute of Technology, Delhi, India

3. Chennai Mathematical Institute & UMI-ReLaX, India

4. Indian Institute of Technology, Hyderabad, Telangana, India

Abstract

We investigate the complexity of languages that correspond to algebraic real numbers, and we present improved upper bounds on the complexity of these languages. Our key technical contribution is the presentation of improved uniform TC 0 circuits for division, matrix powering, and related problems, where the improvement is in terms of “majority depth” (initially studied by Maciel and Thérien). As a corollary, we obtain improved bounds on the complexity of certain problems involving arithmetic circuits, which are known to lie in the counting hierarchy, and we answer a question posed by Yap.

Publisher

IOS Press

Subject

Artificial Intelligence,Computational Theory and Mathematics,Computer Science Applications,Theoretical Computer Science

Reference69 articles.

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