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Electronic Colloquium on Computational Complexity

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Reports tagged with hardness vs randomness:
TR12-080 | 18th June 2012
Baris Aydinlioglu, Dieter van Melkebeek

Nondeterministic Circuit Lower Bounds from Mildly Derandomizing Arthur-Merlin Games

In several settings derandomization is known to follow from circuit lower bounds that themselves are equivalent to the existence of pseudorandom generators. This leaves open the question whether derandomization implies the circuit lower bounds that are known to imply it, i.e., whether the ability to derandomize in *any* way implies ... more >>>

TR21-080 | 10th June 2021
Lijie Chen, Roei Tell

Hardness vs Randomness, Revised: Uniform, Non-Black-Box, and Instance-Wise

We propose a new approach to the hardness-to-randomness framework and to the promise-BPP=promise-P conjecture. Classical results rely on non-uniform hardness assumptions to construct derandomization algorithms that work in the worst-case, or rely on uniform hardness assumptions to construct derandomization algorithms that work only in the average-case. In both types of ... more >>>

TR22-097 | 3rd July 2022
Lijie Chen, Ron D. Rothblum, Roei Tell

Unstructured Hardness to Average-Case Randomness

The leading technical approach in uniform hardness-to-randomness in the last two decades faced several well-known barriers that caused results to rely on overly strong hardness assumptions, and yet still yield suboptimal conclusions.

In this work we show uniform hardness-to-randomness results that *simultaneously break through all of the known barriers*. Specifically, ... 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 >>>

TR23-076 | 24th May 2023
Lijie Chen, Zhenjian Lu, Igor Carboni Oliveira, Hanlin Ren, Rahul Santhanam

Polynomial-Time Pseudodeterministic Construction of Primes

A randomized algorithm for a search problem is *pseudodeterministic* if it produces a fixed canonical solution to the search problem with high probability. In their seminal work on the topic, Gat and Goldwasser posed as their main open problem whether prime numbers can be pseudodeterministically constructed in polynomial time.

... more >>>

TR23-208 | 21st December 2023
Dean Doron, Edward Pyne, Roei Tell

Opening Up the Distinguisher: A Hardness to Randomness Approach for BPL = L that Uses Properties of BPL

We provide compelling evidence for the potential of hardness-vs.-randomness approaches to make progress on the long-standing problem of derandomizing space-bounded computation.

Our first contribution is a derandomization of bounded-space machines from hardness assumptions for classes of uniform deterministic algorithms, for which strong (but non-matching) lower bounds can be unconditionally proved. ... more >>>

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