Quantified derandomization : how to find water in the ocean
著者
書誌事項
Quantified derandomization : how to find water in the ocean
（Foundations and trends in theoretical computer science, 15:1）
Now Publishers, c2022
- : pbk.
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注記
Includes bibliographical references (p. 121-131)
内容説明・目次
内容説明
The focus of this monograph is the question of quantified derandomization. Does derandomization of probabilistic algorithms become easier if we only want to derandomize algorithms that err with extremely small probability? How small does this probability need to be in order for the problem's complexity to be affected?
In this comprehensive survey of the topic, the author describes the body of knowledge accumulated since the question was first raised in 2014, focusing on the following directions: 1) Hardness vs "quantified" randomness; 2) Improving on the brute-force algorithm for quantified derandomization implies breakthrough circuit lower bounds; 3) Unconditional algorithms for quantified derandomization of low-depth circuits and formulas; 4) Arithmetic quantified derandomization; 5) Limitations of certain black-box techniques and pseudoentropy.
Written for researchers, this monograph provides the readers with a concise overview of all known results, but the author also shows several results that are either new or are strengthenings of others. The author also offers a host of concrete challenges and open questions surrounding quantified derandomization.
目次
1. Introduction
2. A Brief History, and Basic Notions
3. An Overview: What Do We Know?
4. Preliminaries
5. Non-uniform Derandomization
6. Hardness vs Quantified Randomness
7. Quantified Derandomization of Specific Circuit Classes
8. Extractors, Restriction Procedures, and Their Limitations
9. Polynomials That Vanish Extremely Rarely
10. Quantified Derandomization and Pseudoentropy
11. A Host of Concrete Challenges
Acknowledgements
Appendices
References
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