




















Abstract:The paper proposes an implicit (i.e., machine-independent) complexity approach to studying computation by polynomial-size, constant-depth circuits with gates counting modulo a constant through the lens of discrete ordinary differential equations (ODEs). So far, recursion-theoretic characterizations have been provided for functions computed by circuits of constant depth, including gates counting modulo 2 and 6 only (i.e., for the classes FAC0[2] and FAC0[6], resp.). In this paper, it is shown that considering ODE schemas, rather than bounded recursion, allows for a more fine-grained analysis, leading to (uniform) characterizations for all classes FAC0[n] (n \in N), i.e. functions computed by circuits including counting modulo n gates. Inspired by the syntactic form of the ODE schemas, we go further in this direction and present first-order bounded theories for capturing provably total functions in each of these classes.
| Subjects: | Computational Complexity (cs.CC) |
| Cite as: | arXiv:2605.23805 [cs.CC] |
| (or arXiv:2605.23805v1 [cs.CC] for this version) | |
| https://doi.org/10.48550/arXiv.2605.23805 arXiv-issued DOI via DataCite (pending registration) |
From: Melissa Antonelli [view email]
[v1]
Fri, 22 May 2026 16:06:37 UTC (55 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。