Bandyopadhyay, Debmalya (2022) Two Conjectures in the Analysis of Boolean Functions. Masters thesis, Indian Institute of Science Education and Research Kolkata.
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Text (MS dissertation of Debmalya Bandyopadhyay (17MS041))
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Abstract
The two main conjectures this report discusses are the Sensitivity Conjecture, and an implication of the Fourier Entropy Influence Conjecture. The Sensitivity Conjecture was recently solved using combinatorial techniques, and we review the work leading up to and following Huang’s ingenious proof. In relation to the Fourier Entropy Influence conjecture, we study flat, homogeneous and Boolean functions for the first time and discuss their properties. We completely solve the 4 term case and present a new way of generating such functions from a 4 term function. Furthermore, we suggest two combinatorial models that may be useful to solve the conjectures involving these functions.
| Item Type: | Thesis (Masters) |
|---|---|
| Additional Information: | Supervisor: Dr. Sourav Chakraborty (Associate Professor, Advanced Computing and Microelectronics Unit, Indian Statistical Institute) |
| Uncontrolled Keywords: | Boolean Functions; Fourier Entropy Influence Conjecture; Sensitivity Conjecture |
| Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science |
| Divisions: | Department of Mathematics and Statistics |
| Depositing User: | IISER Kolkata Librarian |
| Date Deposited: | 19 Apr 2023 10:53 |
| Last Modified: | 19 Apr 2023 10:53 |
| URI: | http://eprints.iiserkol.ac.in/id/eprint/1253 |
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