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REPORTS > KEYWORD > SPACE-BOUNDED DERANDOMIZATION:
Reports tagged with Space-bounded Derandomization:
TR13-086 | 13th June 2013
Omer Reingold, Thomas Steinke, Salil Vadhan

Pseudorandomness for Regular Branching Programs via Fourier Analysis

Revisions: 1

We present an explicit pseudorandom generator for oblivious, read-once, permutation branching programs of constant width that can read their input bits in any order. The seed length is $O(\log^2 n)$, where $n$ is the length of the branching program. The previous best seed length known for this model was $n^{1/2+o(1)}$, ... more >>>


TR21-048 | 27th March 2021
William Hoza

Better Pseudodistributions and Derandomization for Space-Bounded Computation

Revisions: 1

Three decades ago, Nisan constructed an explicit pseudorandom generator (PRG) that fools width-$n$ length-$n$ read-once branching programs (ROBPs) with error $\varepsilon$ and seed length $O(\log^2 n + \log n \cdot \log(1/\varepsilon))$ (Combinatorica 1992). Nisan's generator remains the best explicit PRG known for this important model of computation. However, a recent ... more >>>


TR21-108 | 22nd July 2021
Edward Pyne, Salil Vadhan

Limitations of the Impagliazzo--Nisan--Wigderson Pseudorandom Generator against Permutation Branching Programs

The classic Impagliazzo--Nisan--Wigderson (INW) psesudorandom generator (PRG) (STOC `94) for space-bounded computation uses a seed of length $O(\log n \cdot \log(nwd/\varepsilon))$ to fool ordered branching programs of length $n$, width $w$, and alphabet size $d$ to within error $\varepsilon$. A series of works have shown that the analysis of the ... more >>>


TR23-036 | 27th March 2023
Dean Doron, Roei Tell

Derandomization with Minimal Memory Footprint

Existing proofs that deduce BPL=L from circuit lower bounds convert randomized algorithms into deterministic algorithms with large constant overhead in space. We study space-bounded derandomization with minimal footprint, and ask what is the minimal possible space overhead for derandomization.
We show that $BPSPACE[S] \subseteq DSPACE[c \cdot S]$ for $c \approx ... more >>>


TR23-040 | 28th March 2023
Edward Pyne, Ran Raz, Wei Zhan

Certified Hardness vs. Randomness for Log-Space

Let $\mathcal{L}$ be a language that can be decided in linear space and let $\epsilon >0$ be any constant. Let $\mathcal{A}$ be the exponential hardness assumption that for every $n$, membership in $\mathcal{L}$ for inputs of length~$n$ cannot be decided by circuits of size smaller than $2^{\epsilon n}$.
We ... more >>>


TR23-211 | 23rd December 2023
Rafael Pass, Oren Renard

Characterizing the Power of (Persistent) Randomness in Log-space

We study the problem of whether \emph{persistent} randomness is helpful for polynomial-time algorithms that only use \emph{logarithmic} space. In more detail, we consider the class $\searchBPLs$, of \emph{search}-problems that are solvable by a polynomial-time Probabilistic Logspace TMs with \emph{2-way} access (i.e., with multiple, as opposed to one-time, access) to a ... more >>>


TR24-048 | 4th March 2024
Kuan Cheng, Yichuan Wang

$BPL\subseteq L-AC^1$

Whether $BPL=L$ (which is conjectured to be equal), or even whether $BPL\subseteq NL$, is a big open problem in theoretical computer science. It is well known that $L-NC^1\subseteq L\subseteq NL\subseteq L-AC^1$. In this work we will show that $BPL\subseteq L-AC^1$, which was not known before. Our proof is based on ... more >>>


TR24-090 | 12th May 2024
Gil Cohen, Dean Doron, Tomer Manket, Edward Pyne, Yichuan Wang, Tal Yankovitz

A Study of Error Reduction Polynomials

Error reduction procedures play a crucial role in constructing weighted PRGs [PV'21, CDRST'21], which are central to many recent advances in space-bounded derandomization. The fundamental method driving error reduction procedures is the Richardson iteration, which is adapted from the literature on fast Laplacian solvers. In the context of space-bounded derandomization, ... more >>>




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