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DNF sparsification and a faster deterministic counting algorithm

2013
*
Computational Complexity
*

We give

doi:10.1007/s00037-013-0068-6
fatcat:2jwkc47lv5cy3ciwnezyg2arpa
*a**faster**deterministic**algorithm*for approximately*counting*the number of satisfying solutions to*a**DNF*or CNF. ... Given*a**DNF*(or CNF) f on n variables*and*poly(n) terms, we give*a**deterministic*nÕ ((log log n) 2 ) time*algorithm*that computes an (additive) ε approximation to the fraction of satisfying assignments ... ACKNOWLEDGEMENTS We thank Adam Klivans, Rocco Servedio, Avi Wigderson*and*David Zuckerman for valuable discussions. We thank Rocco for drawing our attention to Friedgut's theorem in this context. ...##
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DNF Sparsification and a Faster Deterministic Counting Algorithm
[article]

2012
*
arXiv
*
pre-print

We combine our

arXiv:1205.3534v1
fatcat:e23ypu6yafgzni35gvz6eqzqgi
*sparsification*result with the work of Luby*and*Velikovic to give*a**faster**deterministic**algorithm*for approximately*counting*the number of satisfying solutions to*a**DNF*. ... Given*a**DNF*formula on n variables, the two natural size measures are the number of terms or size s(f),*and*the maximum width of*a*term w(f). ... Acknowledgements We thank Adam Klivans, Ryan O'Donnell, Rocco Servedio, Avi Wigderson*and*David Zuckerman for valuable discussions. ...##
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DNF Sparsification and a Faster Deterministic Counting Algorithm

2012
*
2012 IEEE 27th Conference on Computational Complexity
*

We give

doi:10.1109/ccc.2012.38
dblp:conf/coco/GopalanMR12
fatcat:zavqxtjwcbaqjlzswy4guu7zzi
*a**faster**deterministic**algorithm*for approximately*counting*the number of satisfying solutions to*a**DNF*or CNF. ... Given*a**DNF*(or CNF) f on n variables*and*poly(n) terms, we give*a**deterministic*nÕ ((log log n) 2 ) time*algorithm*that computes an (additive) ε approximation to the fraction of satisfying assignments ... ACKNOWLEDGEMENTS We thank Adam Klivans, Rocco Servedio, Avi Wigderson*and*David Zuckerman for valuable discussions. We thank Rocco for drawing our attention to Friedgut's theorem in this context. ...##
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Special Issue "Conference on Computational Complexity 2012" Guest editors' foreword

2013
*
Computational Complexity
*

On sunflowers

doi:10.1007/s00037-013-0070-z
fatcat:nosn2cjygrcixofcfvqonshuni
*and*matrix multiplication ... These papers were selected for invitation by the program committee from all the papers presented at the conference,*and*following submission underwent the standard refereeing process. ...*DNF**sparsification**and**a**faster**deterministic**counting*algo One of the hallmarks of computational complexity has been the interplay between*algorithms**and*lower bounds. ...##
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Counting Solutions to Polynomial Systems via Reductions

2018
*
ACM-SIAM Symposium on Discrete Algorithms
*

The approximate-

doi:10.4230/oasics.sosa.2018.6
dblp:conf/soda/Williams18a
fatcat:ojjepy2sijd47b2wtzfqrksrtu
*counting**algorithm*yields efficient approximate*counting*for other well-known problems, such as 2-SAT, NAE-3SAT,*and*3-Coloring. ... We apply this reduction to give*a**deterministic*poly(n, s, log p)/ε 2 -time*algorithm*for approximately*counting*the fraction of solutions to*a*system of s quadratic n-variate polynomials over F p (the ... There, I got*a*chance to think more carefully about the ideas in the approximate*counting**algorithm*. ...##
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Fighting Perebor: New and Improved Algorithms for Formula and QBF Satisfiability

2010
*
2010 IEEE 51st Annual Symposium on Foundations of Computer Science
*

We investigate the possibility of finding satisfying assignments to Boolean formulae

doi:10.1109/focs.2010.25
dblp:conf/focs/Santhanam10
fatcat:kwv6bp73jfe6dmm5rn3byo324a
*and*testing validity of quantified Boolean formulae (QBF) asymptotically*faster*than*a*brute force search. ... Our second main result is*a**deterministic**algorithm*running in time 2 n−Ω(n/ log(n)) for solving QBFs in which the number of occurrences of any variable is bounded by*a*constant. ... For any integer k*and*structured set S of instances, there is*a**deterministic**algorithm*solving k-bounded TQBF which runs in time 2 n−Ω(n) on S. ...##
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The Complexity of Propositional Proofs

2007
*
Bulletin of Symbolic Logic
*

Questions about proof sizes have connections with computational complexity, theories of arithmetic,

doi:10.2178/bsl/1203350879
fatcat:mzffx4yqzfcg7ell47v452f2eu
*and*satisfiability*algorithms*. ... This is article includes*a*broad survey of the field,*and**a*technical exposition of some recently developed techniques for proving lower bounds on proof sizes. ... Thanks also go to Sam Buss for*a*helpful conversation on I∆ 0 ,*and*Jakob Nordström for providing comments on an early draft. ...##
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How many qubits are needed for quantum computational supremacy?

2020
*
Quantum
*

an n×n integer-valued matrix,

doi:10.22331/q-2020-05-11-264
fatcat:6sjufj3vlbe3zeehesaf2v7gi4
*and*assert that any non-*deterministic**algorithm*that solves them requires 2cn time steps, where c∈{*a*,b}. ... Our first two conjectures poly3-NSETH(*a*)*and*per-int-NSETH(b) take specific classical*counting*problems related to the number of zeros of*a*degree-3 polynomial in n variables over F2 or the permanent of ... Finally, we acknowledge Richard Kueng for suggesting the proof strategy in Lemma 9, as well as Tomoyuki Morimae*and*Suguru Tamaki for comments on*a*draft of this paper. ...##
###
How many qubits are needed for quantum computational supremacy?
[article]

2020
*
arXiv
*
pre-print

Each version is parameterized by

arXiv:1805.05224v3
fatcat:vaypbyiqerao7n4ym7owfvxy3e
*a*constant*a**and*asserts that certain specific computational problems with input size n require 2^an time steps to be solved by*a*non-*deterministic**algorithm*. ... with 208 qubits, Quantum Approximate Optimization*Algorithm*(QAOA) circuits with 420 qubits*and*boson sampling circuits (i.e. linear optical networks) with 98 photons are large enough for the task of ... Finally, we acknowledge Richard Kueng for suggesting the proof strategy in Lemma 9, as well as Tomoyuki Morimae*and*Suguru Tamaki for comments on*a*draft of this paper. ...##
###
A Satisfiability Algorithm for Some Class of Dense Depth Two Threshold Circuits

2015
*
IEICE transactions on information and systems
*

We construct

doi:10.1587/transinf.2014edp7127
fatcat:ocjj6xlifbasvee6rtghqrgene
*a*nontrivial*algorithm*for*a*larger class of circuits. ... We give*a*nontrivial circuit satisfiability*algorithm*for*a*class of circuits which may not be sparse in gates with dependency. ... In what follows, we give*a*way to obtain Theorem 3.1 from Lemma 3.1.*A*way to get*a**deterministic**algorithm*from*a*two sided error*algorithm*with error probability at most 1/3 is given as follows. ...##
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The Quantum Strong Exponential-Time Hypothesis
[article]

2019
*
arXiv
*
pre-print

gap between verifier

arXiv:1911.05686v2
fatcat:5qjdfoboofhjbo7c2n6jzvpxji
*and*prover. ... This hypothesis*and*its variants gave rise to*a*fruitful field of research, fine-grained complexity, obtaining (mostly tight) lower bounds for many problems in P whose unconditional lower bounds are hard ... HB, SP,*and*FS are additionally supported by NWO Gravitation grants NETWORKS*and*QSC,*and*EU grant QuantAlgo. ...##
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On Moderately Exponential Time for SAT
[chapter]

2010
*
Lecture Notes in Computer Science
*

., in time p(|F |) 2 cn for some polynomial p

doi:10.1007/978-3-642-14186-7_27
fatcat:vwu4po4v7jac7n4ifktf3wqctu
*and*some constant c < 1, where F is*a*CNF formula of size |F | over n variables? This challenging question is far from being resolved. ... The extension is obtained by allowing*a*∀ . . . ∀ ∃ . . . ∃ prefix in the first-order part. ... Acknowledgment We are grateful to the anonymous referees for their careful analysis*and*valuable suggestions. We implemented most of the suggestions in the final version. ...##
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Quantum Computing: Lecture Notes
[article]

2022
*
arXiv
*
pre-print

The first 10 chapters cover the circuit model

arXiv:1907.09415v4
fatcat:c6g6boiwqzhglbzkkmjlt65upe
*and*the main quantum*algorithms*(Deutsch-Jozsa, Simon, Shor, Hidden Subgroup Problem, Grover, quantum walks, Hamiltonian simulation*and*HHL). ... Appendices*A**and*B give*a*brief introduction to the required linear algebra*and*some other mathematical*and*computer science background. ... One can think of*a*randomized*algorithm*as*a*probability distribution over*deterministic**algorithms*(one*deterministic**algorithm*for each setting of the coins). • When we say*a*(randomized or quantum) ...##
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Improved Bounds for Quantified Derandomization of Constant-Depth Circuits and Polynomials * †

*
48 Leibniz International Proceedings in Informatics Schloss Dagstuhl-Leibniz-Zentrum für Informatik
*
unpublished

For constant-depth circuits, we construct an

fatcat:44jnfppkujal5ik6q2dfui5s2e
*algorithm*for quantified derandomization that works for*a*parameter B(n) that is only slightly smaller than*a*"threshold" parameter,*and*is significantly*faster*... Intuitively,*a*standard technique to*deterministically*find*a*"good" object is to construct*a*simple*deterministic*test that decides the set of good objects,*and*then "fool" that test using*a*pseudorandom ... The author thanks his advisor, Oded Goldreich, for many helpful discussions,*and*for his guidance*and*support during the research*and*writing process. ...##
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st Symposium on Simplicity in Algorithms New Orleans LA, USA Co-located with The 29th ACM-SIAM Symposium on Discrete Algorithms (SODA 2018)

2018
unpublished

Ravi

fatcat:tvuaojfsvjgfjaj7en2x4wdbhy
*and*Madhur Tulsiani for helpful discussions*and*comments on the presentation. Acknowledgement. ... We are very grateful to Dana Ron*and*Oded Goldreich for valuable discussions*and*comments. Acknowledgements. We thank the anonymous reviewers, especially reviewer 2, for their Acknowledgments. ... SIAM, 2017. doi:10.1137/1.9781611974782.143. 28 Michael Luby*and*Boban Velickovic. On*deterministic*approximation of*DNF*. ...
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