تقرير
Beyond Natural Proofs: Hardness Magnification and Locality
| العنوان: | Beyond Natural Proofs: Hardness Magnification and Locality |
|---|---|
| المؤلفون: | Chen, Lijie, Hirahara, Shuichi, Oliveira, Igor C., Pich, Jan, Rajgopal, Ninad, Santhanam, Rahul |
| سنة النشر: | 2019 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Computational Complexity, Computer Science - Discrete Mathematics, Mathematics - Combinatorics |
| الوصف: | Hardness magnification reduces major complexity separations (such as $\mathsf{\mathsf{EXP}} \nsubseteq \mathsf{NC}^1$) to proving lower bounds for some natural problem $Q$ against weak circuit models. Several recent works [OS18, MMW19, CT19, OPS19, CMMW19, Oli19, CJW19a] have established results of this form. In the most intriguing cases, the required lower bound is known for problems that appear to be significantly easier than $Q$, while $Q$ itself is susceptible to lower bounds but these are not yet sufficient for magnification. In this work, we provide more examples of this phenomenon, and investigate the prospects of proving new lower bounds using this approach. In particular, we consider the following essential questions associated with the hardness magnification program: Does hardness magnification avoid the natural proofs barrier of Razborov and Rudich [RR97]? Can we adapt known lower bound techniques to establish the desired lower bound for $Q$? |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1911.08297 |
| رقم الأكسشن: | edsarx.1911.08297 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |