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DOI: 10.4230/LIPIcs.ICALP.2018.36
URN: urn:nbn:de:0030-drops-90401
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9040/
Chillara, Suryajith ; Limaye, Nutan ; Srinivasan, Srikanth
A Quadratic Size-Hierarchy Theorem for Small-Depth Multilinear Formulas
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Abstract
We show explicit separations between the expressive powers of multilinear formulas of small-depth and all polynomial sizes.Formally, for any s = s(n) = n^{O(1)} and any delta>0, we construct explicit families of multilinear polynomials P_n in F[x_1,...,x_n] that have multilinear formulas of size s and depth three but no multilinear formulas of size s^{1/2-delta} and depth o(log n/log log n).
As far as we know, this is the first such result for an algebraic model of computation.
Our proof can be viewed as a derandomization of a lower bound technique of Raz (JACM 2009) using epsilon-biased spaces.
BibTeX - Entry
@InProceedings{chillara_et_al:LIPIcs:2018:9040,
author = {Suryajith Chillara and Nutan Limaye and Srikanth Srinivasan},
title = {{A Quadratic Size-Hierarchy Theorem for Small-Depth Multilinear Formulas}},
booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
pages = {36:1--36:13},
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/2018/9040},
URN = {urn:nbn:de:0030-drops-90401},
doi = {10.4230/LIPIcs.ICALP.2018.36},
annote = {Keywords: Algebraic circuit complexity, Multilinear formulas, Lower Bounds}
}
| Keywords: | Algebraic circuit complexity, Multilinear formulas, Lower Bounds | |
| Seminar: | 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 04.07.2018 |
