A Logical Characterization of Constant-Depth Circuits over the Reals
Computational Complexity
2023-03-16 v3
Abstract
In this paper we give an Immerman's Theorem for real-valued computation. We define circuits operating over real numbers and show that families of such circuits of polynomial size and constant depth decide exactly those sets of vectors of reals that can be defined in first-order logic on R-structures in the sense of Cucker and Meer. Our characterization holds both non-uniformily as well as for many natural uniformity conditions.
Keywords
Cite
@article{arxiv.2005.04916,
title = {A Logical Characterization of Constant-Depth Circuits over the Reals},
author = {Timon Barlag and Heribert Vollmer},
journal= {arXiv preprint arXiv:2005.04916},
year = {2023}
}
Comments
45 pages, submitted to WoLLIC 2021 special issue of Journal of Logic and Computation