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references.bib
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@InProceedings{ a05,
author = {Manindra Agrawal},
booktitle = {\FSTTCS{2005}},
pages = {92-105},
title = {{P}roving {L}ower {B}ounds {V}ia {P}seudo-random
{G}enerators},
year = {2005},
doi = {10.1007/11590156_6}
}
@Article{ ajmv98,
author = {Eric Allender and Jia Jiao and Meena Mahajan and V.
Vinay},
journal = {Theoretical Computer Science},
number = {1-2},
pages = {47-86},
title = {{N}on-{C}ommutative {A}rithmetic {C}ircuits: {D}epth
{R}eduction and {S}ize {L}ower {B}ounds},
volume = {209},
year = {1998},
doi = {10.1016/S0304-3975(97)00227-2}
}
@Article{ Alo09,
address = {New York, NY, USA},
author = {Alon, Noga},
journal = {Combinatorics, Probability and Computing},
month = mar,
number = {1-2},
pages = {3--15},
publisher = {Cambridge University Press},
title = {Perturbed Identity Matrices Have High Rank: Proof and
Applications},
volume = {18},
year = {2009},
doi = {10.1017/S0963548307008917},
issn = {0963-5483}
}
@InProceedings{ av08,
author = {Manindra Agrawal and V. Vinay},
booktitle = {\FOCS{2008}},
pages = {67-75},
title = {Arithmetic Circuits: A Chasm at Depth Four},
year = {2008},
doi = {10.1109/FOCS.2008.32}
}
@InProceedings{ BC15,
author = {Suman K. Bera and Amit Chakrabarti},
booktitle = {Conference on Computational Complexity (CCC)},
pages = {183--197},
title = {A Depth-Five Lower Bound for Iterated Matrix
Multiplication},
year = {2015},
doi = {10.4230/LIPIcs.CCC.2015.183}
}
@Book{ bcs97,
author = {Peter B{\"u}rgisser and Michael Clausen and Mohammad A.
Shokrollahi},
publisher = {Springer-Verlag},
series = {Grundlehren der mathematischen Wissenschaften},
title = {{Algebraic Complexity Theory}},
volume = {315},
year = {1997}
}
@Article{ Berk84,
author = {Stuart J. Berkowitz},
journal = {Information Processing Letters},
number = {3},
pages = {147 - 150},
title = {On computing the determinant in small parallel time using
a small number of processors},
volume = {18},
year = {1984},
doi = {10.1016/0020-0190(84)90018-8},
issn = {0020-0190}
}
@Article{ BLS16,
author = {Nikhil Balaji and Nutan Limaye and Srikanth Srinivasan},
journal = {\ECCC},
note = {\parseECCC{TR16-143}},
pages = {143},
title = {An Almost Cubic Lower Bound for
{\(\Sigma\)}{\(\Pi\)}{\(\Sigma\)} Circuits Computing a
Polynomial in {VP}},
volume = {23},
year = {2016},
url = {http://eccc.hpi-web.de/report/2016/143},
toudpate = {all},
}
@Article{ brent74,
address = {New York, NY, USA},
author = {Brent, Richard P.},
journal = {Journal of the ACM},
month = apr,
number = {2},
pages = {201--206},
publisher = {ACM},
title = {The Parallel Evaluation of General Arithmetic
Expressions},
volume = {21},
year = {1974},
doi = {10.1145/321812.321815},
issn = {0004-5411}
}
@Article{ BS83,
author = {Walter Baur and Volker Strassen},
journal = {Theoretical Computer Science},
pages = {317-330},
title = {The Complexity of Partial Derivatives},
volume = {22},
year = {1983},
doi = {10.1016/0304-3975(83)90110-X}
}
@Book{ bur00,
author = {B{\"u}rgisser, Peter},
note = {Online version:
\url{http://math-www.uni-paderborn.de/agpb/work/habil.ps}},
publisher = {Springer},
series = {Algorithms and Computation in Mathematics},
title = {Completeness and Reduction in Algebraic Complexity
Theory},
year = {2000},
isbn = {9783540667520}
}
@Article{ cai1990,
author = {Cai, Jin-Yi},
journal = {Information and Computation},
number = {1},
pages = {119--127},
publisher = {Elsevier},
title = {A note on the determinant and permanent problem},
volume = {84},
year = {1990}
}
@InProceedings{ ccl2008,
author = {Cai, Jin-Yi and Chen, Xi and Li, Dong},
booktitle = {\STOC{2008}},
organization = {ACM},
pages = {491--498},
title = {A quadratic lower bound for the permanent and determinant
problem over any characteristic$\ne$ 2},
year = {2008},
doi = {10.1145/1374376.1374446}
}
@inproceedings{CILM18,
author = {Marco L. Carmosino and
Russell Impagliazzo and
Shachar Lovett and
Ivan Mihajlin},
title = {Hardness Amplification for Non-Commutative Arithmetic Circuits},
booktitle = {\CCC{2018}},
pages = {12:1--12:16},
year = {2018},
crossref = {DBLP:conf/coco/2018},
url = {https://doi.org/10.4230/LIPIcs.CCC.2018.12},
doi = {10.4230/LIPIcs.CCC.2018.12},
toupdate = {journal},
}
@Article{ ckw11,
author = {Xi Chen and Neeraj Kayal and Avi Wigderson},
journal = {Foundation and Trends in Theoretical Computer Science},
title = {{Partial Derivatives in Arithmetic Complexity (and
beyond)}},
year = {2011},
doi = {10.1561/0400000043}
}
@Book{ clo,
author = {Cox, David A.\ and Little, John B.\ and O'Shea, Donal},
publisher = {Springer},
series = {Undergraduate texts in mathematics},
title = {Ideals, Varieties and Algorithms},
year = {2007},
doi = {10.1007/978-0-387-35651-8}
}
@Article{ cm14,
author = {Suryajith Chillara and Partha Mukhopadhyay},
journal = {\STACS{2014}},
title = {{Depth-4 Lower Bounds, Determinantal Complexity : A
Unified Approach}},
year = {2014},
doi = {10.4230/LIPIcs.STACS.2014.239},
toupdate = {journal}
}
@InProceedings{ dmpy12,
author = {Zeev Dvir and Guillaume Malod and Sylvain Perifel and Amir
Yehudayoff},
booktitle = {\STOC{2012}},
note = {\shortECCC{11}{134}},
pages = {615--624},
title = {Separating multilinear branching programs and formulas},
year = {2012},
doi = {10.1145/2213977.2214034},
url = {http://doi.acm.org/10.1145/2213977.2214034}
}
@Article{ DSY09,
author = {Zeev Dvir and Amir Shpilka and Amir Yehudayoff},
journal = {SIAM Journal of Computing},
note = {\pSTOC{2008}},
number = {4},
pages = {1279--1293},
title = {Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic
Circuits},
volume = {39},
year = {2009},
doi = {10.1137/080735850},
url = {http://dx.doi.org/10.1137/080735850}
}
@InProceedings{ EGOW18,
author = {Klim Efremenko and Ankit Garg and Rafael Mendes{ }de
Oliveira and Avi Wigderson},
booktitle = {9th Innovations in Theoretical Computer Science
Conference, {ITCS} 2018, January 11-14, 2018, Cambridge,
MA, {USA}},
pages = {1:1--1:19},
title = {Barriers for Rank Methods in Arithmetic Complexity},
year = {2018},
doi = {10.4230/LIPIcs.ITCS.2018.1},
url = {https://doi.org/10.4230/LIPIcs.ITCS.2018.1},
toudpate = {journal}
}
@Article{ ellison,
author = {W.\hspace{0.04cm}J. Ellison},
journal = {Proceedings of the Cambridge Philosophical Society},
pages = {663--672},
title = {A `Waring's Problem' for homogeneous forms},
volume = {65},
year = {1969},
doi = {10.1017/S0305004100003455}
}
@Article{ fischer,
author = {Ismor Fischer},
journal = {Mathematics Magazine},
number = {1},
pages = {59--61},
title = {Sums of like powers of multivariate linear forms},
volume = {67},
year = {1994}
}
@article{FLMS13,
author = {Herv{\'{e}} Fournier and
Nutan Limaye and
Guillaume Malod and
Srikanth Srinivasan},
title = {Lower Bounds for Depth-4 Formulas Computing Iterated Matrix Multiplication},
journal = {{SIAM} J. Comput.},
volume = {44},
number = {5},
pages = {1173--1201},
year = {2015},
url = {https://doi.org/10.1137/140990280},
doi = {10.1137/140990280},
note = {\pSTOC{2014}}
}
@InProceedings{ FS13,
author = {Michael A. Forbes and Amir Shpilka},
booktitle = {\FOCS{2013}},
pages = {243--252},
title = {Quasipolynomial-Time Identity Testing of Non-commutative
and Read-Once Oblivious Algebraic Branching Programs},
year = {2013},
doi = {10.1109/FOCS.2013.34},
url = {http://dx.doi.org/10.1109/FOCS.2013.34},
toupdate = {journal}
}
@Article{ gkks13,
author = {Ankit Gupta and Pritish Kamath and Neeraj Kayal and
Ramprasad Saptharishi},
journal = {Journal of the ACM},
note = {\pCCC{2013}},
number = {6},
pages = {33:1--33:16},
title = {Approaching the Chasm at Depth Four},
volume = {61},
year = {2014},
url = {http://doi.acm.org/10.1145/2629541}
}
@article{gkks13b,
author = {Ankit Gupta and
Pritish Kamath and
Neeraj Kayal and
Ramprasad Saptharishi},
title = {Arithmetic Circuits: {A} Chasm at Depth 3},
journal = {{SIAM} J. Comput.},
volume = {45},
number = {3},
pages = {1064--1079},
year = {2016},
url = {https://doi.org/10.1137/140957123},
doi = {10.1137/140957123},
note = {\pFOCS{2013}}
}
@Article{ GLSS12,
author = {Dmitry Gavinsky and Shachar Lovett and Michael Saks and
Srikanth Srinivasan},
journal = {CoRR},
title = {A Tail Bound for Read-k Families of Functions},
volume = {abs/1205.1478},
year = 2012,
toupdate = {all},
}
@Article{ gr00,
author = {Dima Grigoriev and Alexander A. Razborov},
journal = {Appl. Algebra Eng. Commun. Comput.},
note = {\pFOCS{1998}},
number = {6},
pages = {465-487},
title = {Exponential Lower Bounds for Depth 3 Arithmetic Circuits
in Algebras of Functions over Finite Fields},
volume = {10},
year = {2000},
doi = {10.1007/s002009900021}
}
@InProceedings{ grigoriev98,
author = {Dima Grigoriev and Marek Karpinski},
booktitle = {\STOC{1998}},
pages = {577--582},
title = {An Exponential Lower Bound for Depth 3 Arithmetic
Circuits},
year = {1998},
doi = {10.1145/276698.276872}
}
@Misc{ gro:SE,
author = {Joshua Grochow},
note = {\url{http://cstheory.stackexchange.com/questions/19261/degree-restriction-for-polynomials-in-mathsfvp/19268#19268}}
}
@Article{ h90,
author = {H{\aa}stad, Johan},
journal = {J. Algorithms},
month = dec,
note = {\pICALP{1989}},
number = {4},
pages = {644--654},
title = {Tensor Rank is NP-complete},
volume = {11},
year = {1990},
doi = {10.1016/0196-6774(90)90014-6},
issn = {0196-6774},
url = {http://dx.doi.org/10.1016/0196-6774(90)90014-6}
}
@Article{ hr18,
author = {Hardy, G. H. and Ramanujan, Srinavasa},
journal = {Proceedings of the London Mathematical Society},
number = {1},
pages = {75-115},
title = {{Asymptotic Formul{\ae} in Combinatory Analysis}},
volume = {s2-17},
year = {1918},
url = {http://ramanujan.sirinudi.org/Volumes/published/ram36.pdf}
}
@InProceedings{ hwy,
author = {Pavel Hrube\v{s} and Avi Wigderson and Amir Yehudayoff},
booktitle = {\STOC{2010}},
pages = {667-676},
title = {Non-commutative circuits and the sum-of-squares problem},
year = {2010},
url = {http://doi.acm.org/10.1145/1806689.1806781},
toupdate = {journal}
}
@Article{ HY11a,
author = {Pavel Hrube\v{s} and Amir Yehudayoff},
journal = {Computational Complexity},
number = {3},
pages = {559--578},
title = {Homogeneous Formulas and Symmetric Polynomials},
volume = {20},
year = {2011}
}
@InProceedings{ HY16,
author = {Pavel Hrube\v{s} and Amir Yehudayoff},
booktitle = {\ICALP{2016}},
note = {\pECCC{15}{164}},
pages = {89:1--89:12},
title = {On Isoperimetric Profiles and Computational Complexity},
year = {2016},
doi = {10.4230/LIPIcs.ICALP.2016.89},
url = {https://doi.org/10.4230/LIPIcs.ICALP.2016.89},
toupdate = {journal}
}
@Article{ Hyafil1978,
author = {Laurent Hyafil},
journal = {SIAM Journal of Computing},
note = {\pSTOC{1978}},
number = {2},
pages = {120--123},
title = {On the Parallel Evaluation of Multivariate Polynomials},
volume = {8},
year = {1979},
doi = {10.1137/0208010},
url = {http://dx.doi.org/10.1137/0208010}
}
@Article{ js82,
author = {Mark Jerrum and Marc Snir},
journal = {Journal of the ACM},
number = {3},
pages = {874-897},
title = {Some Exact Complexity Results for Straight-Line
Computations over Semirings},
volume = {29},
year = {1982},
doi = {10.1145/322326.322341}
}
@InProceedings{ k2,
author = {Neeraj Kayal},
booktitle = {\ECCC TR12-081},
title = {An exponential lower bound for the sum of powers of
bounded degree polynomials},
year = {2012},
url = {\ECCCurl{12}{081}}
}
@Article{ k85,
author = {Kyriakos Kalorkoti},
journal = {SIAM Journal of Computing},
number = {3},
pages = {678-687},
title = {{A Lower Bound for the Formula Size of Rational
Functions}},
volume = {14},
year = {1985},
doi = {10.1137/0214050}
}
@Article{ kalman00,
author = {D. Kalman},
journal = {{Mathematics Magazine}},
number = {4},
pages = {313-315},
title = {{A Matrix Proof of Newton's Identities}},
volume = {73},
year = {2000},
url = {http://www.maa.org/sites/default/files/
269098238822.pdf.bannered.pdf}
}
@InProceedings{ Kayal09,
author = {Neeraj Kayal},
booktitle = {\CCC{2009}},
month = {July},
pages = {184-193},
title = {The Complexity of the Annihilating Polynomial},
year = {2009},
doi = {10.1109/CCC.2009.37},
issn = {1093-0159}
}
@InCollection{ KayalRP,
address = {Basel},
author = {Neeraj Kayal and Ramprasad Saptharishi},
booktitle = {Perspectives in Computational Complexity},
publisher = {Birkh\"{a}user},
title = {A selection of lower bounds for arithmetic circuits},
year = {2014},
doi = {10.1007/978-3-319-05446-9},
url = {http://www.cmi.ac.in/~ramprasad/pubs/lowerbounds_birk.pdf}
}
@InProceedings{ KayalSaha14,
author = {Neeraj Kayal and Chandan Saha},
booktitle = {\CCC{2015}},
pages = {158--208},
title = {Lower Bounds for Depth Three Arithmetic Circuits with
Small Bottom Fanin},
year = {2015},
doi = {10.4230/LIPIcs.CCC.2015.158},
toupdate = {journal}
}
@InProceedings{ KayalSaha15,
author = {Neeraj Kayal and Chandan Saha},
booktitle = {\ECCC TR15-073},
title = {Lower Bounds for Sums of Products of Low arity
Polynomials},
year = {2015},
url = {\ECCCurl{15}{073}},
toupdate = {all}
}
@Article{ ki03,
author = {Valentine Kabanets and Russell Impagliazzo},
journal = {Computational Complexity},
note = {\pSTOC{2003}},
number = {1-2},
pages = {1-46},
title = {{D}erandomizing Polynomial Identity Tests Means Proving
Circuit Lower Bounds},
volume = {13},
year = {2004},
doi = {10.1007/s00037-004-0182-6}
}
@article{KLSS,
author = {Neeraj Kayal and
Nutan Limaye and
Chandan Saha and
Srikanth Srinivasan},
title = {An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas},
journal = {{SIAM} J. Comput.},
volume = {46},
number = {1},
pages = {307--335},
year = {2017},
url = {https://doi.org/10.1137/151002423},
doi = {10.1137/151002423},
note = {\pFOCS{2014}}
}
@Article{ koiran,
author = {Pascal Koiran},
journal = {Theoretical Computer Science},
pages = {56--65},
title = {Arithmetic Circuits: The Chasm at Depth Four Gets Wider},
volume = {448},
year = {2012},
doi = {10.1016/j.tcs.2012.03.041}
}
@InProceedings{ Koutis08,
author = {Ioannis Koutis},
booktitle = {\ICALP{2008}},
pages = {575-586},
title = {Faster Algebraic Algorithms for Path and Packing
Problems},
year = {2008},
doi = {10.1007/978-3-540-70575-8_47}
}
@InProceedings{ KS14,
author = {Mrinal Kumar and Shubhangi Saraf},
booktitle = {\FOCS{2014}},
title = {{On the power of homogeneous depth $4$ arithmetic
circuits}},
year = {2014},
doi = {10.1109/FOCS.2014.46},
toupdate = {journal}
}
@InProceedings{ KS14a,
author = {Mrinal Kumar and Shubhangi Saraf},
booktitle = {\STOC{2014}},
pages = {136--145},
title = {The limits of depth reduction for arithmetic formulas:
it's all about the top fan-in},
year = {2014},
url = {http://doi.acm.org/10.1145/2591796.2591827},
toupdate = {journal},
}
@InProceedings{ ks15,
author = {Neeraj Kayal and Chandan Saha},
booktitle = {\STACS{2015}},
pages = {527--539},
title = {Multi-k-ic Depth Three Circuit Lower Bound},
volume = {30},
year = {2015},
doi = {10.4230/LIPIcs.STACS.2015.527},
toupdate = {journal}
}
@InProceedings{ KS16lowrank,
author = {Mrinal Kumar and Shubhangi Saraf},
booktitle = {\CCC{2016}},
title = {Arithmetic circuits with locally low algebraic rank},
year = {2016},
toupdate = {journal}
}
@InProceedings{ KSS13,
author = {Neeraj Kayal and Chandan Saha and Ramprasad Saptharishi},
booktitle = {\STOC{2014}},
pages = {146--153},
title = {A super-polynomial lower bound for regular arithmetic
formulas},
year = {2014},
url = {http://doi.acm.org/10.1145/2591796.2591847}
}
@inproceedings{kst16,
author = {Neeraj Kayal and
Chandan Saha and
S{\'{e}}bastien Tavenas},
title = {An Almost Cubic Lower Bound for Depth Three Arithmetic Circuits},
booktitle = {\ICALP{2016}},
pages = {33:1--33:15},
year = {2016},
crossref = {DBLP:conf/icalp/2016},
url = {https://doi.org/10.4230/LIPIcs.ICALP.2016.33},
doi = {10.4230/LIPIcs.ICALP.2016.33},
note = {\shortECCC{16}{006}},
toupdate = {journal}
}
@inproceedings{KumarSapt15,
author = {Mrinal Kumar and
Ramprasad Saptharishi},
title = {An Exponential Lower Bound for Homogeneous Depth-5 Circuits over Finite
Fields},
booktitle = {\CCC{2017}},
pages = {31:1--31:30},
year = {2017},
crossref = {DBLP:conf/coco/2017},
url = {https://doi.org/10.4230/LIPIcs.CCC.2017.31},
doi = {10.4230/LIPIcs.CCC.2017.31},
note = {\arXiv{1507.00177}}
}
@inproceedings{KumarSaraf15,
author = {Mrinal Kumar and
Shubhangi Saraf},
title = {Sums of Products of Polynomials in Few Variables: Lower Bounds and
Polynomial Identity Testing},
booktitle = {\CCC{2016}},
pages = {35:1--35:29},
year = {2016},
crossref = {DBLP:conf/coco/2016},
url = {https://doi.org/10.4230/LIPIcs.CCC.2016.35},
doi = {10.4230/LIPIcs.CCC.2016.35},
}
@inproceedings{KV17,
author = {Noga Alon and
Mrinal Kumar and
Ben Lee Volk},
title = {Unbalancing Sets and an Almost Quadratic Lower Bound for Syntactically
Multilinear Arithmetic Circuits},
booktitle = {\CCC{2018}},
pages = {11:1--11:16},
year = {2018},
crossref = {DBLP:conf/coco/2018},
url = {https://doi.org/10.4230/LIPIcs.CCC.2018.11},
doi = {10.4230/LIPIcs.CCC.2018.11},
}
@article{LST21,
author = {Nutan Limaye and
Srikanth Srinivasan and
S{\'{e}}bastien Tavenas},
title = {Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits},
journal = {\ECCC},
note = {\parseECCC{TR21-081}},
volume = {28},
pages = {81},
year = {2021},
url = {https://eccc.weizmann.ac.il/report/2021/081},
}
@misc{MB18,
title={Combinatorial proofs of the Newton-Girard and Chapman-Costas-Santos identities},
author={Sajal Kumar Mukherjee and Sudip Bera},
year={2018},
eprint={1807.11749},
archivePrefix={arXiv},
primaryClass={math.CO}
}
@Article{ mesh1989,
author = {Meshulam, Roy},
journal = {Linear Algebra and its Applications},
pages = {261--271},
publisher = {Elsevier},
title = {On two extremal matrix problems},
volume = {114},
year = {1989}
}
@article{MP08,
author = {Guillaume Malod and
Natacha Portier},
title = {Characterizing Valiant's algebraic complexity classes},
journal = {J. Complexity},
volume = {24},
number = {1},
pages = {16--38},
year = {2008},
url = {https://doi.org/10.1016/j.jco.2006.09.006},
doi = {10.1016/j.jco.2006.09.006},
note = {\pMFCS{2006}},
timestamp = {Fri, 26 May 2017 22:50:48 +0200},
biburl = {https://dblp.org/rec/bib/journals/jc/MalodP08},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@Article{ mr04,
author = {Mignon, Thierry and Ressayre, Nicolas},
journal = {International Mathematics Research Notes},
note = {Available on
\href{http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.106.4910}{\tt
citeseer:10.1.1.106.4910}},
number = {79},
pages = {4241-4253},
title = {{A quadratic bound for the determinant and permanent
problem.}},
volume = {2004},
year = {2004},
doi = {10.1155/S1073792804142566}
}
@InProceedings{ mv97,
author = {Meena Mahajan and V. Vinay},
booktitle = {\SODA{1997}},
note = {Available on
\href{http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.1673}{\tt
citeseer:10.1.1.31.1673}},
pages = {730-738},
title = {A Combinatorial Algorithm for the Determinant},
year = {1997},
url = {http://dl.acm.org/citation.cfm?id=314161.314429}
}
@InProceedings{ nis91,
author = {Noam Nisan},
booktitle = {\STOC{1991}},
note = {Available on
\href{http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.5067}{\tt
citeseer:10.1.1.17.5067}},
pages = {410-418},
title = {{Lower bounds for non-commutative computation}},
year = {1991},
url = {http://doi.acm.org/10.1145/103418.103462}
}
@Article{ nw1997,
author = {Noam Nisan and Avi Wigderson},
journal = {Computational Complexity},
note = {Available on
\href{http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.90.2644}{\tt
citeseer:10.1.1.90.2644}},
number = {3},
pages = {217--234},
title = {Lower bounds on arithmetic circuits via partial
derivatives},
volume = {6},
year = {1997},
doi = {10.1007/BF01294256}
}
@Article{ nw94,
author = {Noam Nisan and Avi Wigderson},
journal = {Journal of Computer and System Sciences},
note = {Available on
\href{http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.8416}{\tt
citeseer:10.1.1.83.8416}},
number = {2},
pages = {149-167},
title = {{Hardness vs Randomness}},
volume = {49},
year = {1994},
doi = {10.1016/S0022-0000(05)80043-1}
}
@Article{ p85,
author = {Pamfilos, P.},
journal = {Acta Mathematica Hungarica},
number = {1},
pages = {95--97},
title = {On the maximum rank of a tensor product},
volume = {45},
year = {1985},
doi = {10.1007/BF01955026},
issn = {1588-2632},
url = {http://dx.doi.org/10.1007/BF01955026}
}
@article{PSS16,
author = {Anurag Pandey and
Nitin Saxena and
Amit Sinhababu},
title = {Algebraic independence over positive characteristic: New criterion
and applications to locally low-algebraic-rank circuits},
journal = {Computational Complexity},
volume = {27},
number = {4},
pages = {617--670},
year = {2018},
url = {https://doi.org/10.1007/s00037-018-0167-5},
doi = {10.1007/s00037-018-0167-5},
}
@Article{ raz-yehudayoff,
author = {Ran Raz and Amir Yehudayoff},
journal = {Computational Complexity},
note = {\pCCC{2008}},
number = {2},
pages = {171-207},
title = {Lower Bounds and Separations for Constant Depth
Multilinear Circuits},
volume = {18},
year = {2009},
doi = {10.1007/s00037-009-0270-8},
toupdate = {journal}
}
@Article{ Raz06,
author = {Ran Raz},
journal = {Theory of Computing},
note = {\pFOCS{2004}},
number = {1},
pages = {121-135},
title = {Separation of Multilinear Circuit and Formula Size},
volume = {2},
year = {2006},
doi = {10.4086/toc.2006.v002a006}
}
@InProceedings{ raz10,
author = {Ran Raz},
booktitle = {\STOC{2010}},
pages = {659-666},
title = {Tensor-rank and lower bounds for arithmetic formulas},
year = {2010},
url = {http://doi.acm.org/10.1145/2535928}
}
@Article{ Raz10elusive,
author = {Ran Raz},
journal = {Theory of Computing},
note = {\pSTOC{2008}},
number = {1},
pages = {135--177},
title = {Elusive Functions and Lower Bounds for Arithmetic
Circuits},
volume = {6},
year = {2010},
url = {http://dx.doi.org/10.4086/toc.2010.v006a007}
}
@Unpublished{ raz10fool,
author = {Ran Raz},
note = {Invited talk at Microsoft Research},
title = {How to fool people to work on circuit lower bounds},
year = {2010},
url = {http://research.microsoft.com/apps/video/default.aspx?
id=140730}
}
@Article{ raz2004,
author = {Ran Raz},
journal = {Journal of the ACM},
note = {\pSTOC{2004}},
number = {2},
title = {Multi-Linear Formulas for Permanent and Determinant are of
Super-Polynomial Size},
volume = {56},
year = {2009},
doi = {10.1145/1502793.1502797}
}
@Article{ razborov87,
author = {Razborov, Alexander A.},
journal = {Mathematical notes of the Academy of Sciences of the
USSR},
number = {4},
pages = {333-338},
title = {Lower bounds on the size of bounded depth circuits over a
complete basis with logical addition},
volume = {41},
year = {1987},
doi = {10.1007/BF01137685},
issn = {0001-4346},
url = {http://dx.doi.org/10.1007/BF01137685}
}
@Article{ rp:beatcs,
author = {Ramprasad Saptharishi},
journal = {Bulletin of the {EATCS}},
title = {Recent Progress on Arithmetic Circuit Lower Bounds},
volume = {114},
year = {2014},
biburl = {http://dblp.uni-trier.de/rec/bib/journals/eatcs/
Saptharishi14},
url = {http://eatcs.org/beatcs/index.php/beatcs/article/view/293}
}
@Article{ RSY08,
author = {Ran Raz and Amir Shpilka and Amir Yehudayoff},
journal = {SIAM Journal of Computing},
note = {\pFOCS{2007}},
number = {4},
pages = {1624-1647},
title = {A lower bound for the size of syntactically multilinear
arithmetic circuits},
volume = {38},
year = {2008},
doi = {10.1137/070707932}
}
@Article{ ry08,
author = {Ran Raz and Amir Yehudayoff},
journal = {Computational Complexity},
number = {4},
pages = {515--535},
title = {Balancing Syntactically Multilinear Arithmetic Circuits},
volume = {17},
year = {2008},
doi = {10.1007/s00037-008-0254-0}
}
@Article{ rys63,
author = {Herbert J. Ryser},
journal = {Mathematical Association of America},
series = {Carus Mathematical Monographs},
title = {Combinatorial Mathematics},
volume = {14},
year = {1963}
}
@Unpublished{ saptharishivinay14,
author = {Ramprasad Saptharishi and V. Vinay},
note = {Unpublished manuscript},
title = {{An alternate proof of Tavenas' depth reduction}},
year = {2014}
}
@InProceedings{ sax08,
author = {Nitin Saxena},
booktitle = {\ICALP{2008}},
pages = {60-71},
title = {{Diagonal Circuit Identity Testing and Lower Bounds}},
year = {2008},
doi = {10.1007/978-3-540-70575-8_6}
}
@Misc{ Srikanth13,
author = {Srikanth Srinivasan},
howpublished = {personal communication},
year = {2013}
}
@Article{ sw2001,
author = {Amir Shpilka and Avi Wigderson},
journal = {Computational Complexity},
note = {\pCCC{1999}},
number = {1},
pages = {1--27},
title = {Depth-3 arithmetic circuits over fields of characteristic
zero},
volume = {10},
year = {2001},
doi = {10.1007/PL00001609}
}
@Article{ sy,
author = {Shpilka, Amir and Yehudayoff, Amir},
journal = {Foundations and Trends in Theoretical Computer Science},
month = {March},
pages = {207--388},
publisher = {Now Publishers Inc.},
title = {Arithmetic Circuits: A survey of recent results and open
questions},
volume = {5},
year = {2010},
issn = {1551-305X},
url = {http://dx.doi.org/10.1561/0400000039}
}
@Article{ Tav13,
author = {S{\'{e}}bastien Tavenas},
journal = {Inf. Comput.},
note = {\pMFCS{2013}},