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Shrinkage of De Morgan Formulae from Quantum Query Complexity [article]

Avishay Tal
2014 Electronic colloquium on computational complexity  
We give a new and improved proof that the shrinkage exponent of de Morgan formulae is 2.  ...  The proof relies on a result from quantum query complexity by [LLS06, HLS07, Rei11]: for any Boolean function f , Q 2 (f ) ≤ O( L(f )), where Q 2 (f ) is the bounded-error quantum query complexity of f  ...  The connection between de Morgan formulae and quantum query complexity was first noted in the work of Laplante, Lee and Szegedy [LLS06] .  ... 
dblp:journals/eccc/Tal14 fatcat:g5e2s2esdrdy3keogm2wtqn2au

Fourier Concentration from Shrinkage

Russell Impagliazzo, Valentine Kabanets
2014 2014 IEEE 29th Conference on Computational Complexity (CCC)  
For a Boolean function f : {0, 1} n → {1, −1} computable by a de Morgan formula of size s, we show that where Γ is the shrinkage exponent for the corresponding class of formulas: Γ = 2 for de Morgan formulas  ...  For Boolean functions computed by de Morgan formulas of subquadratic size or read-once de Morgan formulas, we prove a sharp concentration of the Fourier mass on "small-degree" coefficients.  ...  of this paper.  ... 
doi:10.1109/ccc.2014.39 dblp:conf/coco/ImpagliazzoK14 fatcat:xrlhsaa2x5b2nbn6udykgvzn2a

Fourier Concentration from Shrinkage

Russell Impagliazzo, Valentine Kabanets
2016 Computational Complexity  
For a Boolean function f : {0, 1} n → {1, −1} computable by a de Morgan formula of size s, we show that where Γ is the shrinkage exponent for the corresponding class of formulas: Γ = 2 for de Morgan formulas  ...  For Boolean functions computed by de Morgan formulas of subquadratic size or read-once de Morgan formulas, we prove a sharp concentration of the Fourier mass on "small-degree" coefficients.  ...  of this paper.  ... 
doi:10.1007/s00037-016-0134-y fatcat:czv5akwlnnaubcnhalr2s6nxqq

Shrinkage under Random Projections, and Cubic Formula Lower Bounds for 𝐀𝐂^0 [article]

Yuval Filmus, Or Meir, Avishay Tal
2020 arXiv   pre-print
Håstad showed that any De Morgan formula (composed of AND, OR and NOT gates) shrinks by a factor of O(p^2) under a random restriction that leaves each variable alive independently with probability p [SICOMP  ...  ., Computational Complexity 5(3/4), 1995] holds for inner functions for which the unweighted quantum adversary bound is tight.  ...  Acknowledgements A.T. would like to thank Igor Carboni Oliveira for bringing the question of proving formula size lower bounds for AC 0 to his attention.  ... 
arXiv:2012.02210v2 fatcat:6lf6rsqihjd6rhpripepatwv7a

Negation-limited formulas

Siyao Guo, Ilan Komargodski
2017 Theoretical Computer Science  
We focus on the model of formulas over the De Morgan basis and consider it in a negation-limited setting.  ...  As a result, the shrinkage exponent of formulas that contain a constant number of negation gates is equal to the shrinkage exponent of monotone formulas.  ...  Acknowledgments We thank Avishay Tal for helpful discussions and, in particular, for a discussion that led to the proof of Theorem 3.1.  ... 
doi:10.1016/j.tcs.2016.11.027 fatcat:lvawujcwtbegxkixyxuhy3tzzy

Algorithms and Lower Bounds for De Morgan Formulas of Low-Communication Leaf Gates

Valentine Kabanets, Sajin Koroth, Zhenjian Lu, Dimitrios Myrisiotis, Igor C. Oliveira, Shubhangi Saraf
2020 Computational Complexity Conference  
The class 𝖥𝖮𝖱𝖬𝖴𝖫𝖠[s]∘𝒢 consists of Boolean functions computable by size-s de Morgan formulas whose leaves are any Boolean functions from a class 𝒢.  ...  As a corollary, we get an average-case lower bound for 𝖦𝖨𝖯^k_n against 𝖥𝖮𝖱𝖬𝖴𝖫𝖠[n^{1.99}]∘𝖯𝖳𝖥^{k-1}, i.e., sub-quadratic-size de Morgan formulas with degree-(k-1) PTF (polynomial threshold  ...  construct approximating polynomials for de Morgan formulas which rely only on the existence of such polynomials, without requiring an efficient quantum query algorithm.  ... 
doi:10.4230/lipics.ccc.2020.15 dblp:conf/coco/KabanetsKLMO20 fatcat:jzht3ie3ezg7di7goqaak6z32e

Algorithms and Lower Bounds for de Morgan Formulas of Low-Communication Leaf Gates [article]

Valentine Kabanets, Sajin Koroth, Zhenjian Lu, Dimitrios Myrisiotis, Igor Oliveira
2020 arXiv   pre-print
The class FORMULA[s] ∘G consists of Boolean functions computable by size-s de Morgan formulas whose leaves are any Boolean functions from a class G.  ...  Let R^(k)(G) be the maximum k-party NOF randomized communication complexity of G.  ...  We also thank Mahdi Cheraghchi for several discussions on the analysis of Boolean circuits with a bottom layer of parity gates.  ... 
arXiv:2002.08533v1 fatcat:qfiearqugbaklfftdb2ku7flsa

Computational Complexity of Discrete Problems

Anna Gal, Michal Koucký, Oded Regev, Rüdiger Reischuk
Report from Dagstuhl Seminar   unpublished
This report documents the program and the outcomes of Dagstuhl Seminar 14121 "Computational Complexity of Discrete Problems".  ...  The first section gives an overview of the topics covered and the organization of the meeting. Section 2 lists the talks given in chronological order.  ...  We then present the "group-theoretic" approach of Cohn and Umans as an alternative to these methods, and we generalize this approach from group algebras to general algebras.  ... 
fatcat:hhoeyx6vzncdfcikgmalgm6pby

Introduction – The Contributions of Big Data
Introduction – Les apports des Big Data

Philippe Tassi
2019 Economics and Statistics  
However, we cannot do without some degree of vigilance, since data and how they are used can affect individuals, their freedoms and the preservation of their privacy.  ...  This has encouraged the Big Data phenomenon, the volume of which includes two related parameters: quantity and frequency of acquisition; quantity can extend as far as exhaustivity and frequency can be  ...  of the complexity, 5.  ... 
doi:10.24187/ecostat.2018.505d.1963 fatcat:42rehacy6ffb7hc6k2l2q4u4yy

Coalgebraic Logics (Dagstuhl Seminar 12411) Algebraic and Combinatorial Methods in Computational Complexity (Dagstuhl Seminar 12421) Time-of-Flight Imaging: Algorithms, Sensors and Applications (Dagstuhl Seminar 12431) Foundations and Challenges of Change and Evolution in Ontologies (Dagstuhl Seminar 12441) Requirements Management-Novel Perspectives and Challenges (Dagstuhl Seminar 12442)

Lieven Desmet, Martin Johns, Benjamin Livshits, Andrei Sabelfeld, Ernst-Erich Doberkat, Alexander Kurz, Manindra Agrawal, Thomas Thierauf, Christopher Umans, James Davis, Bernd Jähne, Andreas Kolb (+9 others)
2012 unpublished
In addition, we sketch some approaches for dealing with requirements evolution, adopted from the PhD thesis of Neil Ernst [1].  ...  We then discuss how computational complexity creeps in and how to cope with it.  ...  For de Morgan formulas, seed length s 1/3+o(1) ; 2. For formulas over an arbitrary basis, seed length s 1/2+o(1) ; 3. For read-once de Morgan formulas, seed length s 0.234... ; 4.  ... 
fatcat:3zuf3grgabettljj7apksbc4lq

Derandomizing space-bounded computation via pseudorandom generators and their generalizations [article]

William Michael Hoza, 0000-0001-5162-9181, Austin, The University Of Texas At, David I. Zuckerman
2021
Regarding the PRG approach, we present improved PRGs for interesting models of computation including unbounded-width permutation branching programs, read-once AC⁰ formulas, and superlinear-size constant-depth  ...  Regarding generalizations of PRGs, we present new constructions and applications of HSGs and WPRGs for read-once branching programs (ROBPs), the nonuniform model that directly corresponds to randomized  ...  “Shrinkage of De Morgan Formulae by Spectral Techniques”.  ... 
doi:10.26153/tsw/15500 fatcat:trgrebxcxjfapmyglqgu7k5bne

Sixteenth Critical Bibliography of the History and Philosophy of Science and of the History of Civilization

George Sarton
1925 Isis  
Morgan, Robert Burns (editor). Readings in English social history from yo ye ool! literature. Vol. 1-5. From pre-Roman days to A. D. 1837.  ...  American mathematical monthly, vol. 31, 83, 1924. ists Extract from a letter by De Morgan, dated Oct. 17, i858, « ECLEn’s life, dating from 1736, the year in which his productions began to appear with  ... 
doi:10.1086/358324 fatcat:4riedgzkwrc6nbukkkkukvqdza

Free‐field reciprocity calibration of laboratory standard (LS) microphones using a time selective technique

Knud Rasmussen, Salvador Barrera‐Figueroa
2006 Journal of the Acoustical Society of America  
Acknowledgment of Honolulu Local Meeting Organizing Committees Presentation of Fellowship Certificates  ...  Vector sensor array sensitivity and mismatch: Generalization of the Gilbert-Morgan formula. Andrew J. Poulsen and Arthur B.  ...  We show that the signal travel time is dependent on the behavior of the dispersion formula in the complex frequency plane and place limits on the range of validity of these formulas, leading naturally  ... 
doi:10.1121/1.4788231 fatcat:o5zthkauwvddtjcer4wralkeja

Ultra‐high‐speed imaging of bubbles interacting with cells and tissue

Michel Versluis, Philippe Marmottant, Sascha Hilgenfeldt, Claus‐Dieter Ohl, Chien T. Chin, Annemieke van Wamel, Nico de Jong, Detlef Lohse
2006 Journal of the Acoustical Society of America  
Acknowledgment of Honolulu Local Meeting Organizing Committees Presentation of Fellowship Certificates  ...  Vector sensor array sensitivity and mismatch: Generalization of the Gilbert-Morgan formula. Andrew J. Poulsen and Arthur B.  ...  We show that the signal travel time is dependent on the behavior of the dispersion formula in the complex frequency plane and place limits on the range of validity of these formulas, leading naturally  ... 
doi:10.1121/1.4788217 fatcat:5drbrqyk65cqzff2cmj5ne6n5e

Combinatorics and Algorithmics of Strings (Dagstuhl Seminar 14111) Computational Complexity of Discrete Problems (Dagstuhl Seminar 14121) Computational Models of Cultural Behavior for Human-Agent Interaction (Dagstuhl Seminar 14131) Interaction and Collective Movement Processing (Dagstuhl Seminar 14132) Spatial reference in the Semantic Web and in Robotics (Dagstuhl Seminar 14142)

Johannes Fürnkranz, Eyke Hüllermeier, Cynthia Rudin, Scott Sanner, Roman Słowiński, Maxime Crochemore, James Currie, Gregory Kucherov, Dirk Nowotka, Pierre Dillenbourg, Claude Kirchner, John Mitchell (+25 others)
2014 unpublished
The motivation for this seminar was to showcase recent progress in these different areas with the goal of working towards a common basis of understanding, which should help to facilitate future synergies  ...  This report documents the program and the outcomes of Dagstuhl Seminar 14101 "Preference Learning".  ...  This yields both an implicit characterization of polynomial time in terms of ordinary differential equations, and a completeness result on the reachability problems for the corresponding class.  ... 
fatcat:k3cugkqpf5btlba2hklfxyujdq
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