Abstract
We show that high dimensional expanders imply derandomized direct product tests, with a number of subsets that is linear in the size of the universe.Direct product tests belong to a family of tests called agreement tests that are important components in PCP constructions and include, for example, low degree tests such as line vs. line and plane vs. plane.For a generic hypergraph, we introduce the notion of agreement expansion, which captures the usefulness of the hypergraph for an agreement test. We show that explicit bounded degree agreement expanders exist, based on Ramanujan complexes.
| Original language | English |
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| Title of host publication | Proceedings - 58th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2017 |
| Publisher | IEEE Computer Society |
| Pages | 974-985 |
| Number of pages | 12 |
| ISBN (Electronic) | 9781538634646 |
| DOIs | |
| State | Published - 10 Nov 2017 |
| Event | 58th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2017 - Berkeley, United States Duration: 15 Oct 2017 → 17 Oct 2017 |
Publication series
| Name | Annual Symposium on Foundations of Computer Science - Proceedings |
|---|---|
| Volume | 2017-October |
| ISSN (Print) | 0272-5428 |
Conference
| Conference | 58th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2017 |
|---|---|
| Country/Territory | United States |
| City | Berkeley |
| Period | 15/10/17 → 17/10/17 |
Bibliographical note
Publisher Copyright:© 2017 IEEE.
Keywords
- agreement tests
- direct product
- direct sum
- high dimensional expanders