The DOI matches its Crossref record; 176 of the 176 references it cites were found in a registry or an index.
Analysis of Boolean Functions
Open accessAbstract
Boolean functions are perhaps the most basic objects of study in theoretical computer science. They also arise in other areas of mathematics, including combinatorics, statistical physics, and mathematical social choice. The field of analysis of Boolean functions seeks to understand them via their Fourier transform and other analytic methods. This text gives a thorough overview of the field, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry. Each chapter includes a 'highlight application' such as Arrow's theorem from economics, the Goldreich–Levin algorithm from cryptography/learning theory, Håstad's NP-hardness of approximation results, and 'sharp threshold' theorems for random graph properties. The book includes roughly 450 exercises and can be used as the basis of a one-semester graduate course. It should appeal to advanced undergraduates, graduate students and researchers in computer science theory and related mathematical fields.
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The Theory of Error-Correcting Codes
(1977) · North-Holland Mathematical Library · doi:10.1016/s0924-6509(08)x7030-8 · Cited by 10,760
Einstein, A. (1905) · Annalen der Physik · doi:10.1002/andp.19053220806 · Cited by 8,265
Social Choice and Individual Values.
Shackle, G. L. S., & Arrow, K. J. (1951) · Economica · doi:10.2307/2549613 · Cited by 7,792
Bollobás, B. (1985) · Cited by 6,196
The Byzantine generals problem
Lamport, L., Shostak, R., & Pease, M. (1982) · ACM Transactions on Programming Languages and Systems · doi:10.1145/357172.357176 · Cited by 6,023
Shapley, L. S. (1988) · The Shapley Value · doi:10.1017/cbo9780511528446.003 · Cited by 4,954
On the Theory of the Brownian Motion
Uhlenbeck, G. E., & Ornstein, L. S. (1930) · Physical Review · doi:10.1103/physrev.36.823 · Cited by 4,482
Functions of Bounded Variation and Free Discontinuity Problems
Ambrosio, L., Fusco, N., & Pallara, D. (2000) · doi:10.1093/oso/9780198502456.001.0001 · Cited by 4,318
Spencer, J. (1991) · Medical Entomology and Zoology · Cited by 4,310
Goemans, M. X., & Williamson, D. P. (1995) · Journal of the ACM · doi:10.1145/227683.227684 · Cited by 3,587
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Yeom, S., Giacomelli, I., Fredrikson, M., & Jha, S. (2018) · 2018 IEEE 31st Computer Security Foundations Symposium (CSF) · doi:10.1109/csf.2018.00027 · Cited by 1,001
Achieving quantum supremacy with sparse and noisy commuting quantum computations
Bremner, M. J., Montanaro, A., & Shepherd, D. J. (2017) · Quantum · doi:10.22331/q-2017-04-25-8 · Cited by 191
Guest Column: A Survey of Quantum Learning Theory
Arunachalam, S., & de Wolf, R. (2017) · ACM SIGACT News · doi:10.1145/3106700.3106710 · Cited by 152
Competency Problems: On Finding and Removing Artifacts in Language Data
Gardner, M., Merrill, W., Dodge, J., Peters, M., Ross, A., Singh, S., & Smith, N. A. (2021) · Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing · doi:10.18653/v1/2021.emnlp-main.135 · Cited by 81
Reducing the CNOT count for Clifford+T circuits on NISQ architectures
Gheorghiu, V., Huang, J., Li, S. M., Mosca, M., & Mukhopadhyay, P. (2020) · arXiv · doi:10.48550/arxiv.2011.12191 · Cited by 31
Metadata
- Authors
- O'Donnell, R.
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 2014-06-05
- OpenAlex
- W1891181203
- Cited by
- 932
- References
- 176
- FWCI
- 35.08
- Type
- book
- Language
- en
- Open access
- green
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