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Electronic Colloquium on Computational Complexity

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Reports tagged with Pseudodeterministic algorithms:
TR19-012 | 27th January 2019
Oded Goldreich

Multi-pseudodeterministic algorithms

Revisions: 1

In this work, dedicated to Shafi Goldwasser, we consider a relaxation of the notion of pseudodeterministic algorithms, which was put forward by Gat and Goldwasser ({\em ECCC}, TR11--136, 2011).

Pseudodeterministic algorithms are randomized algorithms that solve search problems by almost always providing the same canonical solution (per each input). ... more >>>

TR21-039 | 15th March 2021
Zhenjian Lu, Igor Carboni Oliveira, Rahul Santhanam

Pseudodeterministic Algorithms and the Structure of Probabilistic Time

We connect the study of pseudodeterministic algorithms to two major open problems about the structural complexity of $BPTIME$: proving hierarchy theorems and showing the existence of complete problems. Our main contributions can be summarised as follows.

1. A new pseudorandom generator and its consequences: We build on techniques developed to ... more >>>

TR23-070 | 9th May 2023
Shuichi Hirahara, Zhenjian Lu, Hanlin Ren

Bounded Relativization

Relativization is one of the most fundamental concepts in complexity theory, which explains the difficulty of resolving major open problems. In this paper, we propose a weaker notion of relativization called *bounded relativization*. For a complexity class $C$, we say that a statement is *$C$-relativizing* if the statement holds relative ... 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 >>>

TR23-144 | 22nd September 2023
Lijie Chen, Shuichi Hirahara, Hanlin Ren

Symmetric Exponential Time Requires Near-Maximum Circuit Size

We show that there is a language in $\mathrm{S}_2\mathrm{E}/_1$ (symmetric exponential time with one bit of advice) with circuit complexity at least $2^n/n$. In particular, the above also implies the same near-maximum circuit lower bounds for the classes $\Sigma_2\mathrm{E}$, $(\Sigma_2\mathrm{E}\cap\Pi_2\mathrm{E})/_1$, and $\mathrm{ZPE}^{\mathrm{NP}}/_1$. Previously, only "half-exponential" circuit lower bounds for these ... more >>>

TR23-156 | 26th October 2023
Zeyong Li

Symmetric Exponential Time Requires Near-Maximum Circuit Size: Simplified, Truly Uniform

Revisions: 1

In a recent breakthrough, Chen, Hirahara and Ren prove that S$_2$E/$_1 \not\subset$ SIZE$[2^n/n]$ by giving a single-valued FS$_2$P algorithm for the Range Avoidance Problem (Avoid) that works for infinitely many input size $n$.

Building on their work, we present a simple single-valued FS$_2$P algorithm for Avoid that works for all ... more >>>

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