Year: 2026
Type: preprint
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 the following results. 1. When $n \le w$, we show an SC derandomization with space $O(\log^2 n+\log w)$ and two-sided error $1/\text{poly}(nw)$. 2. When $n \ge w$, we show an SC derandomization with space $O(\log n \log w)$ and two-sided error $1/\text{poly}(w)$. In addition, when $w=O(\log n)$, we attain an optimal $O(\log n)$ space derandomization with two-sided error $1/\text{poly}(w)$. 3. When $w \le 2^{O(\sqrt{\log n})}$, we show that reachability of regular ROBPs (i.e. derandmization of one-sided unbounded small error ROBPs) can be computed in SC. We also show that when regular ROBPs are powering, optimal deterministic logspace can be attained for computing reachability and for bounded two-sided error derandomization, when $w = n^{1/c}$ for some constant $c$. 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).
Source: arXiv (Cornell University)
Authors: Cheng, Kuan, Wu, Ruiyang
Institution: Peking University
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214013034
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