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DOI: 10.4230/LIPIcs.ICALP.2018.54
URN: urn:nbn:de:0030-drops-90582
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9058/
Forbes, Michael A. ; Ghosh, Sumanta ; Saxena, Nitin
Towards Blackbox Identity Testing of Log-Variate Circuits
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Abstract
Derandomization of blackbox identity testing reduces to extremely special circuit models. After a line of work, it is known that focusing on circuits with constant-depth and constantly many variables is enough (Agrawal,Ghosh,Saxena, STOC'18) to get to general hitting-sets and circuit lower bounds. This inspires us to study circuits with few variables, eg. logarithmic in the size s.We give the first poly(s)-time blackbox identity test for n=O(log s) variate size-s circuits that have poly(s)-dimensional partial derivative space; eg. depth-3 diagonal circuits (or Sigma wedge Sigma^n). The former model is well-studied (Nisan,Wigderson, FOCS'95) but no poly(s2^n)-time identity test was known before us. We introduce the concept of cone-closed basis isolation and prove its usefulness in studying log-variate circuits. It subsumes the previous notions of rank-concentration studied extensively in the context of ROABP models.
BibTeX - Entry
@InProceedings{forbes_et_al:LIPIcs:2018:9058,
author = {Michael A. Forbes and Sumanta Ghosh and Nitin Saxena},
title = {{Towards Blackbox Identity Testing of Log-Variate Circuits}},
booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
pages = {54:1--54:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-076-7},
ISSN = {1868-8969},
year = {2018},
volume = {107},
editor = {Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9058},
URN = {urn:nbn:de:0030-drops-90582},
doi = {10.4230/LIPIcs.ICALP.2018.54},
annote = {Keywords: hitting-set, depth-3, diagonal, derandomization, polynomial identity testing, log-variate, concentration, cone closed, basis isolation}
}
| Keywords: | hitting-set, depth-3, diagonal, derandomization, polynomial identity testing, log-variate, concentration, cone closed, basis isolation | |
| Seminar: | 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 04.07.2018 |
