Simulation-based approaches for understanding conjectures in cs-theory
| dc.contributor.author | Madhani, Omar | |
| dc.date.accessioned | 2022-09-09T20:51:38Z | |
| dc.date.available | 2022-09-09T20:51:38Z | |
| dc.date.copyright | 2022 | en_US |
| dc.date.issued | 2022-09-09 | |
| dc.description.abstract | Given an algorithmic problem, what is the time taken by the best algorithm solving the problem? With hopes to get closer to answering this question, we discuss restricting algorithms into weaker decision tree models where inputs are queried one bit at a time. We explore how lifting theorems can lift the lower bounds of the query complexity to a stronger communication complexity model; from here we can compute the efficiency of the original algorithm in terms of communication cost. This poster describes a conjecture based on the Index Function and its implications on the lifting theorem if proved. The disperser property conjecture of the Index Function has been proven to be false when m < log_2(n) and true when m > n*log_2(n). We explain the natural computational limitations of a numerical simulation-based approach to prove the disperser property conjecture when log_2(n) <= m <= n*log_2(n). The poster offers experimental techniques, including efficient pseudo-random sampling of the Index gadget’s pointer/string subset and a linear program to verify the monotone version of the disperser property conjecture. | en_US |
| dc.description.reviewstatus | Reviewed | en_US |
| dc.description.scholarlevel | Undergraduate | en_US |
| dc.description.sponsorship | Valerie Kuehne Undergraduate Research Awards (VKURA) | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/14237 | |
| dc.language.iso | en | en_US |
| dc.subject | theoretical computer science | en_US |
| dc.subject | communication complexity | en_US |
| dc.subject | computer simulation | en_US |
| dc.subject | mathematical conjecture | en_US |
| dc.subject | disperser property | en_US |
| dc.subject | pseudo-randomness | en_US |
| dc.subject | linear programming | en_US |
| dc.subject | SageMath | en_US |
| dc.title | Simulation-based approaches for understanding conjectures in cs-theory | en_US |
| dc.type | Poster | en_US |