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Hardness Amplification Via Space-Efficient Direct Products [chapter]

Venkatesan Guruswami, Valentine Kabanets
2006 Lecture Notes in Computer Science  
The proof of our Direct Product Lemma is inspired by Dinur's remarkable proof of the PCP theorem by gap amplification using expanders [Din05] .  ...  We prove a version of the derandomized Direct Product Lemma for deterministic spacebounded algorithms.  ...  Introduction Hardness amplification via Direct Products Hardness amplification is, roughly, a procedure for converting a somewhat difficult computational problem into a much more difficult one.  ... 
doi:10.1007/11682462_52 fatcat:udzsfvvkhjgnfadcb2torhj2hi

Hardness Amplification via Space-Efficient Direct Products

Venkatesan Guruswami, Valentine Kabanets
2008 Computational Complexity  
The proof of our Direct Product Lemma is inspired by Dinur's remarkable proof of the PCP theorem by gap amplification using expanders [Din05] .  ...  We prove a version of the derandomized Direct Product Lemma for deterministic spacebounded algorithms.  ...  Introduction Hardness amplification via Direct Products Hardness amplification is, roughly, a procedure for converting a somewhat difficult computational problem into a much more difficult one.  ... 
doi:10.1007/s00037-008-0253-1 fatcat:m4dcekzmgvggzlqo3ln2ay6a5y

Approximately List-Decoding Direct Product Codes and Uniform Hardness Amplification

Russell Impagliazzo, Ragesh Jaiswal, Valentine Kabanets
2006 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)  
Such codes arise naturally in the context of hardness amplification of Boolean functions via Yao's Direct Product Lemma (and closely related Yao's XOR Lemma), where typically k N (e.g., k = poly log N  ...  We consider the problem of locally list-decoding direct product codes.  ...  Uniform hardness amplification The main application of the Direct Product Lemma (or Yao's XOR Lemma) is to hardness amplification: If a Boolean function f is somewhat hard to compute on average, its XOR  ... 
doi:10.1109/focs.2006.13 dblp:conf/focs/ImpagliazzoJK06 fatcat:zeep23bc2bddzistnauntnvwvu

Approximate List-Decoding of Direct Product Codes and Uniform Hardness Amplification

Russell Impagliazzo, Ragesh Jaiswal, Valentine Kabanets
2009 SIAM journal on computing (Print)  
We give an efficient randomized algorithm for approximate local list-decoding of direct product codes.  ...  As an application of our decoding algorithm, we get uniform hardness amplification for P NP , the class of languages reducible to NP through one round of parallel oracle queries: If there is a language  ...  Proof of the direct product amplification. Here we prove Lemma 8. For convenience, we restate it below. Lemma 8 (direct product amplification).  ... 
doi:10.1137/070683994 fatcat:z6lo3xkqszdtnchhpi2f3iit2a

Hardness Amplification of Optimization Problems

Elazar Goldenberg, Karthik C. S., Michael Wagner
2020 Innovations in Theoretical Computer Science  
In this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products.  ...  Given a direct product feasible optimization problem Π, our hardness amplification theorem may be informally stated as follows: If there is a distribution D over instances of Π of size n such that every  ...  Remark about Direct Product results and Hardness Amplification The direct product lemma at the heart of most hardness amplification results is the XOR lemma [34] .  ... 
doi:10.4230/lipics.itcs.2020.1 dblp:conf/innovations/GoldenbergS20 fatcat:nqnlm74n65f7tm22q4hetqiiv4

Hardness Amplification of Optimization Problems [article]

Elazar Goldenberg, Karthik C. S.
2019 arXiv   pre-print
In this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products.  ...  Given a direct product feasible optimization problem Π, our hardness amplification theorem may be informally stated as follows: If there is a distribution D over instances of Π of size n such that every  ...  Remark about Direct Product results and Hardness Amplification. The direct product lemma at the heart of most hardness amplification results is the XOR lemma [Yao82] .  ... 
arXiv:1908.10248v1 fatcat:x64xa7v64fex7btlaepayxlqui

Counterexamples to Hardness Amplification beyond Negligible [chapter]

Yevgeniy Dodis, Abhishek Jain, Tal Moran, Daniel Wichs
2012 Lecture Notes in Computer Science  
A natural approach to hardness amplification is the "direct product"; instead of asking an attacker to solve a single instance of a problem, we ask the attacker to solve several independently generated  ...  Interestingly, proving that the direct product amplifies hardness is often highly non-trivial, and in some cases may be false. For example, it is known that the direct product (i.e.  ...  Attacking the Direct-Product. Let us now briefly demonstrate an adversary A for the k-wise direct product.  ... 
doi:10.1007/978-3-642-28914-9_27 fatcat:5ymfaplisrbdzme473du47w3ai

Hardness Amplification Proofs Require Majority

Ronen Shaltiel, Emanuele Viola
2010 SIAM journal on computing (Print)  
Our results reveal a contrast between Yao's XOR Lemma (Amp(f ) : (1) and (2) apply to Yao's XOR lemma, whereas known proofs of the direct-product lemma violate both (1) and (2) .  ...  Hardness amplification is the fundamental task of converting a δ-hard function f : {0, 1} n → {0, 1} into a (1/2 − )-hard function Amp(f ), where f is γ-hard if small circuits fail to compute f on at least  ...  Ronen would like to thank Avi Wigderson for introducing him to the subject of hardness amplification and for many discussions.  ... 
doi:10.1137/080735096 fatcat:bhl5645ylbeoblgoy4j3r5sta4

Hardness amplification proofs require majority

Ronen Shaltiel, Emanuele Viola
2008 Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08  
Our results reveal a contrast between Yao's XOR Lemma (Amp(f ) : (1) and (2) apply to Yao's XOR lemma, whereas known proofs of the direct-product lemma violate both (1) and (2) .  ...  Hardness amplification is the fundamental task of converting a δ-hard function f : {0, 1} n → {0, 1} into a (1/2 − )-hard function Amp(f ), where f is γ-hard if small circuits fail to compute f on at least  ...  Ronen would like to thank Avi Wigderson for introducing him to the subject of hardness amplification and for many discussions.  ... 
doi:10.1145/1374376.1374461 dblp:conf/stoc/ShaltielV08 fatcat:vff7uzc2ijd3bmzccuzwhzbe3q

A method for extracting DNA from hard tissues for use in forensic identification

Jarunya Samsuwan, Thanutham Somboonchokepisal, Thunyathorn Akaraputtiporn, Tunwarut Srimuang, Phuris Phuengsukdaeng, Aunchulee Suwannarat, Apiwat Mutirangura, Nakarin Kitkumthorn
2018 Biomedical Reports  
With deceased and decayed bodies, personal identification is performed using hard tissue DNA, commonly extracted from bone.  ...  Finally, it was indicated that components of seawater may inhibit PCR amplification.  ...  The results from a selection of the DNA samples were confirmed by direct sequencing of the PCR products (16) to verify the sequence accuracy.  ... 
doi:10.3892/br.2018.1148 pmid:30402227 pmcid:PMC6200996 fatcat:7pjojkbxmzbpdh4w2p5xveknxq

Allelic composition of puroindolinium genes and confectionery properties of flour of soft winter wheat samples

О. Ю. Леонов, Я. Ю. Шарипіна, З. В. Усова, К. Ю. Суворова, Т. В. Сахно
2020 Plant Varieties Studying and Protection  
Identification of soft winter wheat varieties and lines from the Plant Production Institute nd. a. V. Ya.  ...  As to Pinb-D1 gene, all hard grain samples had Pinb-D1b allele, and the 'Erythrospermum S 424-1/14' line was heterogeneous for Pinb-D1a/Pinb-D1b.  ...  The absence of the amplification product on the electrophoregram corre- (Fig. 1) .  ... 
doi:10.21498/2518-1017.16.2.2020.209258 fatcat:th7qqa2cqzg75c7w26q5zmmwm4

On the Complexity of Parallel Hardness Amplification for One-Way Functions [chapter]

Chi-Jen Lu
2006 Lecture Notes in Computer Science  
We prove complexity lower bounds for the tasks of hardness amplification of one-way functions and construction of pseudo-random generators from one-way functions, which are realized non-adaptively in black-box  ...  In fact, one can derive from such an amplification procedure a highly parallel one-way function, which is computable by an NC 0 circuit (constant-depth polynomialsize circuit with bounded fan-in gates)  ...  This explains why the security preserving hardness amplification procedures of [7, 4] are sequential while the parallel hardness amplification procedure by direct product [21] blows up the input length  ... 
doi:10.1007/11681878_24 fatcat:r6hxlyrqgrdj3llukccdstxs3e

Uniform direct product theorems

Russell Impagliazzo, Ragesh Jaiswal, Valentine Kabanets, Avi Wigderson
2008 Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08  
As a direct consequence of this generalization we obtain the first derandomized direct product result in the uniform setting, allowing hardness amplification with only constant (as opposed to a factor  ...  The classical Direct-Product Theorem for circuits says that if a Boolean function f : {0, 1} n → {0, 1} is somewhat hard to compute on average by small circuits, then the corresponding k-wise direct product  ...  Direct-product theorems are a primary tool in hardness amplification, allowing one to convert problems that are somewhat hard into problems that are more reliably hard.  ... 
doi:10.1145/1374376.1374460 dblp:conf/stoc/ImpagliazzoJKW08 fatcat:hf7oot3cvnazzpjg24e2h5ugbm

On Hardness Amplification of One-Way Functions [chapter]

Henry Lin, Luca Trevisan, Hoeteck Wee
2005 Lecture Notes in Computer Science  
The "direct product" construction is a simple approach to prove amplification of hardness results.  ...  It is easy to check that F satisfies all of the 3 properties, from which hardness amplification via direct product follows.Random Walk on Expanders.  ... 
doi:10.1007/978-3-540-30576-7_3 fatcat:syhbtwc4obc4xkrqls4iired2e

The bang for the buck

Wei Lu, Francesco Bonchi, Amit Goyal, Laks V.S. Lakshmanan
2013 Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '13  
We show that the fair seed allocation problem is NP-hard, and develop an efficient algorithm called Needy Greedy.  ...  The key algorithmic problem in viral marketing is to identify a set of influential users (called seeds) in a social network, who, when convinced to adopt a product, shall influence other users in the network  ...  As a case study, we focus on minimizing the maximum amplification factor offered to companies ( §3.2). • We show that FSA under K-LT model is NP-hard ( §4.1).  ... 
doi:10.1145/2487575.2487649 dblp:conf/kdd/LuB0L13 fatcat:k64guifby5hqhahne5ffghfb4u
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