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In this paper we motivate the study of Boolean dispersers for quadratic varieties by showing that an explicit construction of such objects gives improved circuit lower bounds. An (n; k; s)-quadratic disperser is a function on n variables that is not constant on any subset of Fn2 of size at least s that can be defined as the set of common roots of at most k quadratic polynomials. We show thfi at if a Boolean function f is a n; 1:83n; 2g(n)-quadratic disperser for any function g(n) = o(n) then the circuit size of f is at least 3:11n. In order to prove this, we generalize the gate elimination method so that the induction works on the size of the variety rather than on the number of variables as in previously known proofs.
Язык оригинала | английский |
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Название основной публикации | ITCS 2016 - Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science |
Издатель | Association for Computing Machinery |
Страницы | 405-411 |
Число страниц | 7 |
ISBN (электронное издание) | 9781450340571 |
DOI | |
Состояние | Опубликовано - 14 янв 2016 |
Событие | 7th ACM Conference on Innovations in Theoretical Computer Science, ITCS 2016 - Cambridge, Соединенные Штаты Америки Продолжительность: 14 янв 2016 → 16 янв 2016 |
Название | ITCS 2016 - Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science |
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конференция | 7th ACM Conference on Innovations in Theoretical Computer Science, ITCS 2016 |
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Страна/Tерритория | Соединенные Штаты Америки |
Город | Cambridge |
Период | 14/01/16 → 16/01/16 |
ID: 49824036