21st Annual IEEE Conference on Computational Complexity (CCC'06)最新文献

On modular counting with polynomials 关于多项式的模计数

21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.29

Kristoffer Arnsfelt Hansen

引用次数: 6

New Lower Bounds for Vertex Cover in the Lovasz-Schrijver Hierarchy Lovasz-Schrijver层次中顶点覆盖的新下界

21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.28

Iannis Tourlakis

{"title":"New Lower Bounds for Vertex Cover in the Lovasz-Schrijver Hierarchy","authors":"Iannis Tourlakis","doi":"10.1109/CCC.2006.28","DOIUrl":"https://doi.org/10.1109/CCC.2006.28","url":null,"abstract":"Lovdsz and Schrijver (1991) defined three progressively stronger procedures LS0, LS and LS+, for systematically tightening linear relaxations over many rounds. All three procedures yield the integral hull after at most n rounds. On the other hand, constant rounds of LS+ can derive the relaxations behind many famous approximation algorithms such as those for MAX-CUT, SPARSEST-CUT. So proving round lower bounds for these procedures on specific problems may give evidence about inapproximability. We prove new round lower bounds for vertex cover in the LS hierarchy. Arora et al. (2006) showed that the integrality gap for VERTEX COVER relaxations remains 2 - o(1) even after Omega(log n) rounds LS. However, their method can only prove round lower bounds as large as the girth of the input graph, which is O(log n) for interesting graphs. We break through this \"girth barrier\" and show that the integrality gap for VERTEX COVER remains 1.5 - epsi even after Omega(log2 n) rounds of LS. In contrast, the best PCP-based results only rule out 1.36-approximations. Moreover, we conjecture that the new technique we introduce to prove our lower bound, the \"fence\" method, may lead to linear or nearly linear LS round lower bounds for VERTEX COVER","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126254133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 33

Exposure-resilient extractors Exposure-resilient萃取器

21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.19

Marius Zimand

引用次数: 7

Minimizing DNF formulas and AC/sup 0//sub d/ circuits given a truth table 最小化DNF公式和给定真值表的AC/sup 0//sub /电路

21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.27

E. Allender, L. Hellerstein, Paul McCabe, T. Pitassi, M. Saks

{"title":"Minimizing DNF formulas and AC/sup 0//sub d/ circuits given a truth table","authors":"E. Allender, L. Hellerstein, Paul McCabe, T. Pitassi, M. Saks","doi":"10.1109/CCC.2006.27","DOIUrl":"https://doi.org/10.1109/CCC.2006.27","url":null,"abstract":"For circuit classes R, the fundamental computational problem Min-R asks for the minimum R-size of a Boolean function presented as a truth table. Prominent examples of this problem include Min-DNF, which asks whether a given Boolean function presented as a truth table has a k-term DNF, and Min-Circuit (also called MCSP), which asks whether a Boolean function presented as a truth table has a size k Boolean circuit. We present a new reduction proving that Min-DNF is NP-complete. It is significantly simpler than the known reduction of Masek (1979), which is from Circuit-SAT. We then give a more complex reduction, yielding the result that Min-DNF cannot be approximated to within a factor smaller than (log N)Upsi, for some constant Upsi > 0, assuming that NP is not contained in quasipolynomial time. The standard greedy algorithm for set cover is often used in practice to approximate Min-DNF. The question of whether Min-DNF can be approximated to within a factor of o(log N) remains open, but we construct an instance of Min-DNF on which the solution produced by the greedy algorithm is Omega(log N) larger than optimal. Finally, we extend known hardness results for Min-TC0 d to obtain new hardness results for Min-AC 0 d, under cryptographic assumptions","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121141417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 19

Circuit lower bounds via Ehrenfeucht-Fraisse games 电路下界通过Ehrenfeucht-Fraisse游戏

21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.12

M. Koucký, C. Lautemann, S. Poloczek, D. Thérien

引用次数: 21

On the complexity of numerical analysis 论数值分析的复杂性

21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.30

E. Allender, Peter Bürgisser, Johan Kjeldgaard-Pedersen, Peter Bro Miltersen

引用次数: 181

A generic time hierarchy for semantic models with one bit of advice 带有一点建议的语义模型的通用时间层次结构

21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.7

D. Melkebeek, Konstantin Pervyshev

{"title":"A generic time hierarchy for semantic models with one bit of advice","authors":"D. Melkebeek, Konstantin Pervyshev","doi":"10.1109/CCC.2006.7","DOIUrl":"https://doi.org/10.1109/CCC.2006.7","url":null,"abstract":"We show that for any reasonable semantic model of computation and for any positive integer a and rationals 1 < c < d, there exists a language computable in time nd with a bits of advice but not in time nc with a bits of advice. A semantic model is one for which there exists a computable enumeration that contains all machines in the model but may also contain others. We call such a model reasonable if it has an efficient universal machine that can be complemented within the model in exponential time and if it is efficiently closed under deterministic transducers. Our result implies the first such hierarchy theorem for randomized machines with zero-sided error, quantum machines with one- or zero-sided error, unambiguous machines, symmetric alternation, Arthur-Merlin games of any signature, etc. Our argument yields considerably simpler proofs of known hierarchy theorems with one bit of advice for randomized and quantum machines with two-sided error. Our paradigm also allows us to derive stronger separation results in a unified way. For models that have an efficient universal machine that can be simulated deterministically in exponential time and that are efficiently closed under randomized reductions with two-sided error, we establish the following: For any constants a and c, there exists a language computable in polynomial time with one bit of advice but not in time nc with a log n bits of advice. The result applies to randomized and quantum machines with two-sided error. For randomized machines with one-sided error, our approach yields that for any constants a and c there exists a language computable in polynomial time with one bit of advice but not in time nc with a (log n)1c/ bits of advice","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"397 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115214733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 22

Applications of the sum-product theorem in finite fields 和积定理在有限域中的应用

21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.9

A. Wigderson

引用次数: 0

Optimal hardness results for maximizing agreements with monomials 最佳硬度结果，以最大限度地与单项协议

21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.31

Vitaly Feldman

{"title":"Optimal hardness results for maximizing agreements with monomials","authors":"Vitaly Feldman","doi":"10.1109/CCC.2006.31","DOIUrl":"https://doi.org/10.1109/CCC.2006.31","url":null,"abstract":"We consider the problem of finding a monomial (or a term) that maximizes the agreement rate with a given set of examples over the Boolean hypercube. The problem is motivated by learning of monomials in the agnostic framework of Haussler (Hastad, 2001) and Kearns et al. (1994). Finding a monomial with the highest agreement rate was proved to be NP-hard by Kearns and Li (1993). Ben-David et al. gave the first inapproximability result for this problem, proving that the maximum agreement rate is NP-hard to approximate within 770/767 - epsi, for any constant epsi > 0 (Ben-David et al., 2003). The strongest known hardness of approximation result is due to Bshouty and Burroughs, who proved an inapproximability factor of 59/58 - epsi (2002). We show that the agreement rate NP-hard to approximate within 2 - epsi for any constant epsi > 0. This is optimal up to the second order terms and resolves an open question due to Blum (2002). We extend this result to epsi = 2-log1-lambda;n for any constant lambda > 0 under the assumption that NP nsube RTIME(npoly log(n)), thus also obtaining an inapproximability factor of 2log1-lambda n for the symmetric problem of minimizing disagreements. This improves on the log n hardness of approximation factor due to Kearns et al. (1994) and Hoffgen et al. (1995)","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124798524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 31

Distinguishing SAT from polynomial-size circuits, through black-box queries 区分SAT从多项式大小的电路，通过黑盒查询

21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.17

Albert Atserias

引用次数: 21