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Distributed Verification and Hardness of Distributed Approximation [article]

Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, Roger Wattenhofer
2011 arXiv   pre-print
Moreover, our unconditional lower bound of approximating minimum spanning tree (MST) subsumes and improves upon the previous hardness of approximation bound of Elkin [STOC 2004] as well as the lower bound  ...  In this paper we initiate a systematic study of distributed verification, and give almost tight lower bounds on the running time of distributed verification algorithms for many fundamental problems such  ...  , i.e., hardness of distributed approximation.  ... 
arXiv:1011.3049v3 fatcat:wctqtam435hxldsbeh2apbt3fy

Distributed Verification and Hardness of Distributed Approximation

Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, Roger Wattenhofer
2012 SIAM journal on computing (Print)  
Distributed Algorithms, Approximation, and Hardness.  ...  , i.e., hardness of distributed approximation.  ...  Bounds on Hardness of Distributed Approximation. An important consequence of our verification lower bound is that it leads to lower bounds for exact and approximate distributed computation.  ... 
doi:10.1137/11085178x fatcat:xkvkvn6hlnh6vi4f56szewjv4m

Distributed verification and hardness of distributed approximation

Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, Roger Wattenhofer
2011 Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11  
Distributed Algorithms, Approximation, and Hardness.  ...  , i.e., hardness of distributed approximation.  ...  Bounds on Hardness of Distributed Approximation. An important consequence of our verification lower bound is that it leads to lower bounds for exact and approximate distributed computation.  ... 
doi:10.1145/1993636.1993686 dblp:conf/stoc/SarmaHKKNPPW11 fatcat:igixoskxrbhntjdntoox7snmnq

Probabilistic Programming: A True Verification Challenge [chapter]

Joost-Pieter Katoen
2015 Lecture Notes in Computer Science  
Formal semantics and verification. In this invited talk, I will survey recent progress on the formal semantics and verification of (parametric) probabilistic programs.  ...  The aim is to study the computational hardness of these problems as well as to develop (semi-) algorithms and accompanying tool-support.  ...  This work is funded by the EU FP7-projects SENSATION and MEALS, and the Excellence Initiative of the German federal and state government.  ... 
doi:10.1007/978-3-319-24953-7_1 fatcat:i7bwx2oaufguhpzbedvqoap26m

Quantum computational supremacy

Aram W. Harrow, Ashley Montanaro
2017 Nature  
Here we present the leading proposals to achieve quantum supremacy, and discuss how we can reliably compare the power of a classical computer to the power of a quantum computer.  ...  The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer.  ...  . • Terhal and DiVincenzo: 8 This paper gave the first complexity-theoretic argument that a simple class of quantum circuits should be hard to simulate classically. • Aaronson and Arkhipov: 9 This seminal  ... 
doi:10.1038/nature23458 pmid:28905912 fatcat:fkzk4t6hc5eu7e7zjracqplsz4

Lattice signatures using NTRU on the hardness of worst-case ideal lattice problems

Dipayan Das, Vishal Saraswat, Kajla Basu
2020 IET Information Security  
The security of these signature schemes depends mainly on the hardness of solving short integer solutions (SIS) and/or learning with errors problem in the random oracle model.  ...  Both the signature and the verification are done efficiently by doing polynomial convolutions in the ring ℤ[x]/(x n + 1).  ...  So, the size of the signature is approximately mnlog 5r.  ... 
doi:10.1049/iet-ifs.2019.0580 fatcat:j2p6w2uy4nb6xndxl3qn5znco4

A signature scheme from Learning with Truncation [article]

Jeffrey Hoffstein, Jill Pipher, William Whyte, Zhenfei Zhang
2017 IACR Cryptology ePrint Archive  
The most significant new contribution, enabled by this Gaussian sampling version of pqNTRUSign, is that we can now perform batch verification, which allows the verifier to check approximately 2000 signatures  ...  in a single verification process.  ...  It has been shown in [5] that the decisional LWR q,r,n,m problem is hard assuming the hardness of LWE q,r,n,m with parameters m ≥ log(q) log(2γ) • m and q ≥ γ(nmβp) for some γ ≥ 1.  ... 
dblp:journals/iacr/HoffsteinPWZ17 fatcat:3nk7zjs3ofbsvhgaodhjz32zpa

Boson Sampling with Gaussian input states: efficient scaling and certification [article]

Raphael A. Abrahao, Austin P. Lund
2021 arXiv   pre-print
We propose the use of switchable dual-homodyne and single-photon detections, the temporal loop technique and scattershot based Boson Sampling.  ...  Furthermore, this particular combination of techniques permits a single efficient implementation of Boson Sampling and efficient certification in a single experimental setup.  ...  Despite advances in understanding the effect of losses [21] [22] [23] [48] [49] [50] [51] [52] [53] , there remains a gap between the necessary and sufficient criterion for the hardness of approximate  ... 
arXiv:1812.08978v4 fatcat:kv7xubentzh7fp4twhogenolya

Embed and Project: Discrete Sampling with Universal Hashing

Stefano Ermon, Carla P. Gomes, Ashish Sabharwal, Bart Selman
2013 Neural Information Processing Systems  
We demonstrate that by using state-of-the-art combinatorial search tools, PAWS can efficiently sample from Ising grids with strong interactions and from software verification instances, while MCMC and  ...  distribution.  ...  We consider the fundamental problem of (approximately) sampling from p(x), i.e., designing a randomized algorithm that takes w as input and outputs elements x ∈ X according to the probability distribution  ... 
dblp:conf/nips/ErmonGSS13 fatcat:3sfucsgamzfrjick63y4cyeemy

A game of quantum advantage: linking verification and simulation [article]

Daniel Stilck França, Raul Garcia-Patron
2022 arXiv   pre-print
Beyond this setting, by employing strong data processing inequalities, our framework allows us to analyse the effect of noise on classical simulability and verification of more general near-term quantum  ...  First, for random quantum circuits, Bob being able to efficiently distinguish his distribution from Alice's implies efficient approximate simulation of the distribution.  ...  RGP was supported by the Quantum Computing and Simulation Hub, an EPSRC-funded project, part of the UK National Quantum Technologies Programme.  ... 
arXiv:2011.12173v2 fatcat:5trgxg2qg5dt3ipopizqkrtufq

Input Validation for Neural Networks via Runtime Local Robustness Verification [article]

Jiangchao Liu, Liqian Chen, Antoine Mine, Ji Wang
2020 arXiv   pre-print
Another observation is that the robustness radii of correctly classified inputs often follow a normal distribution.  ...  Experiments show that our approach can protect neural networks from adversarial examples and improve their accuracies.  ...  ., 2017) and robustness (Ehlers, 2017; Dutta et al., 2018) . However, due to the non-linearity of activation functions, complete verification is NP-hard, and thus can hardly scale.  ... 
arXiv:2002.03339v1 fatcat:hxogvcxshba7pax7s2tcigovcm

Approximate String Membership Checking: A Multiple Filter, Optimization-Based Approach

Chong Sun, Jeffrey F. Naughton, Siddharth Barman
2012 2012 IEEE 28th International Conference on Data Engineering  
Furthermore, in our experiments we found that in some cases a sequence of filters dominates any of the filters of the sequence in isolation, and that the best set of filters and their ordering depend upon  ...  Accordingly, we propose that the approximate match problem be viewed as an optimization problem, and evaluate a number of techniques for solving this optimization problem.  ...  The token distribution filter in [11] compares the token distributions of two strings to determine whether they can approximately match or not.  ... 
doi:10.1109/icde.2012.68 dblp:conf/icde/SunNB12 fatcat:op5bx74jlna55b3kdtszflkvha

Sum-of-Squares meets Nash: Optimal Lower Bounds for Finding any Equilibrium [article]

Pravesh K. Kothari, Ruta Mehta
2018 arXiv   pre-print
They can then adaptively construct a list of candidate solutions and invoke a verification oracle to check if any candidate on the list is a solution.  ...  The state-of-the-art algorithms for computing exact and approximate equilibria in two-player, n-strategy games are captured in this model and require that at least one of i) size ( running time) of the  ...  Acknowledgement We thank the anonymous reviewers for pointing out typos and missed references and giving useful suggestions for better presentation.  ... 
arXiv:1806.09426v1 fatcat:bxqoxselcbednpo3i64ehflu5m

PCPs and the Hardness of Generating Private Synthetic Data [chapter]

Jonathan Ullman, Salil Vadhan
2011 Lecture Notes in Computer Science  
of whose two-way marginals are approximately equal to those of D.  ...  We also present both negative and positive results for generating "relaxed" synthetic data, where the fraction of rows in D satisfying a predicate c are estimated by applying c to each row of D and aggregating  ...  Acknowledgments We thank Boaz Barak, Irit Dinur, Cynthia Dwork, Vitaly Feldman, Oded Goldreich, Johan Håstad, Valentine Kabanets, Dana Moshkovitz, Anup Rao, Guy Rothblum, and Les Valiant for helpful conversations  ... 
doi:10.1007/978-3-642-19571-6_24 fatcat:mj7l5ogyqzcrxf62lyy7cu3di4

Effects of abrasive size distribution in chemical mechanical planarization: Modeling and verification

Jianfeng Luo, D.A. Dornfeld
2003 IEEE transactions on semiconductor manufacturing  
A material removal rate formulation as a function of abrasive size distribution is proposed and verified.  ...  Based on the model, the abrasive size distribution influences the material removal from two aspects, one, the number of active abrasives, and the other, the size of the active abrasives.  ...  ACKNOWLEDGMENT The authors appreciate the detailed comments of the reviewers.  ... 
doi:10.1109/tsm.2003.815199 fatcat:jcgmgipzb5d5doeqegiicxqx2y
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