SC Derandomization for Regular ROBPs and Models Beyond BPL

2026-09-20

AI Summary

研究解决了正则一次读分支程序（ROBPs）及超越BPL模型的SC去随机化问题，通过不同条件下空间复杂度与错误率控制的方法实现。

Abstract

We study SC derandomizations for regular read-once branching programs (ROBPs) and computation models beyond BPL. For regular ROBPs with length $n$, width $w$, and multiple accept nodes, we attain three results. 1. When $n \le w$, we show an SC derandomization with space $O(\log^2 n+\log w)$ and error $1/\text{poly}(nw)$. 2. When $n \ge w$, we show an SC derandomization with space $O(\log n \log w)$ and error $1/\text{poly}(w)$. 3. When $w=O(\log n)$, we show an optimal $O(\log n)$ space derandomization with error $1/\text{poly}(w)$. We further show that two super sets of BPL can be computed in SC. 1. For probabilistic logspace TMs with a two-way access random tape, we show that it can be approximated in SC if each entry of the random tape is accessed for at most a constant number of times. 2. For probabilistic logspace TMs with a polynomial size stack, i.e. probabilistic logspace Auxiliary Push-down Machines (AuxPDMs), we show that it can be approximated in SC if the timings of push/pop/idle stack operations do not depend on the randomness. The first model is the read-multiplicity model considered by Impagliazzo, Nisan, Wigderson (STOC'94), in which they show that their INW generator can fool such computations. For the second model, we indicate that it contains candidate languages separating BQL from BPL considered by Apers and Edenhofer (CCC'25).

Problem

• SC derandomization
• regular ROBPs
• BPL
• computation models
• probabilistic logspace TMs

Innovation

• SC Derandomization
• Regular ROBPs
• BPL Supersets
• Probabilistic Logspace TMs
• AuxPDMs