发布求助
文献互助 智能选刊 最新文献

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

筛选
英文 中文
Making hard problems harder 让难题变得更难
21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.26
Joshua Buresh-Oppenheim, R. Santhanam
{"title":"Making hard problems harder","authors":"Joshua Buresh-Oppenheim, R. Santhanam","doi":"10.1109/CCC.2006.26","DOIUrl":"https://doi.org/10.1109/CCC.2006.26","url":null,"abstract":"We consider a general approach to the hoary problem of (im)proving circuit lower bounds. We define notions of hardness condensing and hardness extraction, in analogy to the corresponding notions from the computational theory of randomness. A hardness condenser is a procedure that takes in a Boolean function as input, as well as an advice string, and outputs a Boolean function on a smaller number of bits which has greater hardness when measured in terms of input length. A hardness extractor takes in a Boolean function as input, as well as an advice string, and outputs a Boolean function defined on a smaller number of bits which has close to maximum hardness. We prove several positive and negative results about these objects. First, we observe that hardness-based pseudo-random generators can be used to extract deterministic hardness from non-deterministic hardness. We derive several consequences of this observation. Among other results, we show that if E/O(n) has exponential non-deterministic hardness, then E/O{n) has deterministic hardness 2n/n, which is close to the maximum possible. We demonstrate a rare downward closure result: E with sub-exponential advice is contained in non-uniform space 2deltan for all delta > 0 if and only if there is k > 0 such that P with quadratic advice can be approximated in non-uniform space nk . Next, we consider limitations on natural models of hardness condensing and extraction. We show lower bounds on the advice length required for hardness condensing in a very general model of \"relativizing\" condensers. We show that non-trivial black-box extraction of deterministic hardness from deterministic hardness is essentially impossible. Finally, we prove positive results on hardness condensing in certain special cases. We show how to condense hardness from a biased function without advice using a hashing technique. We also give a hardness condenser without advice from average-case hardness to worst-case hardness. Our technique uses a connection between hardness condensing and explicit constructions of covering codes","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"15 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":"126678832","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: 11
Learning monotone decision trees in polynomial time 在多项式时间内学习单调决策树
21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1137/060669309
Ryan O'Donnell, R. Servedio
{"title":"Learning monotone decision trees in polynomial time","authors":"Ryan O'Donnell, R. Servedio","doi":"10.1137/060669309","DOIUrl":"https://doi.org/10.1137/060669309","url":null,"abstract":"We give an algorithm that learns any monotone Boolean function f: {-1, 1}n rarr {-1, 1} to any constant accuracy, under the uniform distribution, in time polynomial in n and in the decision tree size of f. This is the first algorithm that can learn arbitrary monotone Boolean functions to high accuracy, using random examples only, in time polynomial in a reasonable measure of the complexity of f. A key ingredient of the result is a new bound showing that the average sensitivity of any monotone function computed by a decision tree of size s must be at most radic(log s). This bound has already proved to be of independent utility in the study of decision tree complexity (Schramm et al., 2005). We generalize the basic inequality and learning result described above in various ways; specifically, to partition size (a stronger complexity measure than decision tree size), p-biased measures over the Boolean cube (rather than just the uniform distribution), and real-valued (rather than just Boolean-valued) functions","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"14 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":"117336905","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: 109
Godel and Computations 哥德尔与计算
21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.21
P. Pudlák
{"title":"Godel and Computations","authors":"P. Pudlák","doi":"10.1109/CCC.2006.21","DOIUrl":"https://doi.org/10.1109/CCC.2006.21","url":null,"abstract":"Godel was born 100 years ago in this country. It is a good opportunity to commemorate this anniversary by a lecture about his influence on computational complexity. He also made contributions on computability, length of proofs, and diagonalization","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"37 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":"134219879","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: 1
Parallel repetition of zero-knowledge proofs and the possibility of basing cryptography on NP-hardness 零知识证明的并行重复和基于np -硬度的密码学的可能性
21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.33
R. Pass
{"title":"Parallel repetition of zero-knowledge proofs and the possibility of basing cryptography on NP-hardness","authors":"R. Pass","doi":"10.1109/CCC.2006.33","DOIUrl":"https://doi.org/10.1109/CCC.2006.33","url":null,"abstract":"Two long-standing open problems exist on the fringe of complexity theory and cryptography: (1) Does there exist a reduction from an NP-complete problem to a one-way function? (2) Do parallelized versions of classical constant-round zero-knowledge proofs for NP conceal every \"hard\" bit of the witness to the statement proved? We show that, unless the polynomial-hierarchy collapses, black-box reductions cannot be used to provide positive answers to both questions","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"50 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":"131467660","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: 27
Derandomization of probabilistic auxiliary pushdown automata classes 概率辅助下推自动机类的非随机化
21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.16
H. Venkateswaran
{"title":"Derandomization of probabilistic auxiliary pushdown automata classes","authors":"H. Venkateswaran","doi":"10.1109/CCC.2006.16","DOIUrl":"https://doi.org/10.1109/CCC.2006.16","url":null,"abstract":"We extend Nisan's breakthrough derandomization result that BP<sub>H</sub>L sube SC<sup>2</sup> (1992) to bounded error probabilistic complexity classes based on auxiliary pushdown automata. In particular, we show that any logarithmic space, polynomial time two-sided bounded-error probabilistic auxiliary pushdown automaton (the corresponding complexity class is denoted by BP<sub>H</sub>LOGCFL) can be simulated by an SC<sup>2</sup> machine. This derandomization result improves a classical result by Cook (1979) that LOGDCFL sube SC<sup>2 </sup> since LOGDCFL is contained in BP<sub>H</sub>LOGCFL. We also present a simple circuit-based proof that BP<sub>H</sub>LOGCFL is in NC <sup>2</sup>","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"109 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":"115268644","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: 5
A 3-query non-adaptive PCP with perfect completeness 具有完全完备性的3查询非自适应PCP
21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.5
Subhash Khot, Rishi Saket
{"title":"A 3-query non-adaptive PCP with perfect completeness","authors":"Subhash Khot, Rishi Saket","doi":"10.1109/CCC.2006.5","DOIUrl":"https://doi.org/10.1109/CCC.2006.5","url":null,"abstract":"We study a very basic open problem regarding the PCP characterization of NP, namely, the power of PCPs with 3 non-adaptive queries and perfect completeness. The lowest soundness known till now for such a PCP is 6/8 + epsi given by a construction of Hastad (1997). However, Zwick (1998) shows that a 3-query non-adaptive PCP with perfect completeness cannot achieve soundness below 5/8. In this paper, we construct a 3-query non-adaptive PCP with perfect completeness and soundness 20/27 + epsi, which improves upon the previous best soundness of 6/8 + epsi. A standard reduction from PCPs to constraint satisfaction problems (CSPs) implies that it is NP-hard to tell if a Boolean CSP on 3-variables has a satisfying assignment or no assignment satisfies more than 20/27 + epsi fraction of the constraints. Our construction uses \"biased long codes\" introduced by Dinur and Safra (2002). We develop new 3-query tests to check consistency between such codes. These tests are analyzed by extending Hastad's Fourier methods (1997) to the biased case","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":"128937058","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: 24
FO[<]-uniformity FO(<)均匀性
21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.20
C. Behle, K. Lange
{"title":"FO[<]-uniformity","authors":"C. Behle, K. Lange","doi":"10.1109/CCC.2006.20","DOIUrl":"https://doi.org/10.1109/CCC.2006.20","url":null,"abstract":"Uniformity notions more restrictive than the usual FO[<, +, *]-uniformity = FO[<, Bit]-uniformity are introduced. It is shown that the general framework exhibited by Barrington et al. still holds if the fan-in of the gates in the corresponding circuits is considered","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"119 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":"122859706","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
QMA/qpoly /spl sube/ PSPACE/poly: de-Merlinizing quantum protocols QMA/qpoly /spl sub / PSPACE/poly:脱梅林化量子协议
21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.36
S. Aaronson
{"title":"QMA/qpoly /spl sube/ PSPACE/poly: de-Merlinizing quantum protocols","authors":"S. Aaronson","doi":"10.1109/CCC.2006.36","DOIUrl":"https://doi.org/10.1109/CCC.2006.36","url":null,"abstract":"This paper introduces a new technique for removing existential quantifiers over quantum states. Using this technique, we show that there is no way to pack an exponential number of bits into a polynomial-size quantum state, in such a way that the value of any one of those bits can later be proven with the help of a polynomial-size quantum witness. We also show that any problem in QMA with polynomial-size quantum advice, is also in PSPACE with polynomial-size classical advice. This builds on our earlier result that BQP/qpoly sube PP/poly, and offers an intriguing counterpoint to the recent discovery of Raz that QIP/qpoly = ALL. Finally, we show that QCMA/qpoly sube PP/poly and that QMA/rpoly = QMA/poly","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"60 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":"123447392","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: 18
Grid graph reachability problems 网格图可达性问题
21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.22
E. Allender, D. M. Barrington, T. Chakraborty, Samir Datta, Sambuddha Roy
{"title":"Grid graph reachability problems","authors":"E. Allender, D. M. Barrington, T. Chakraborty, Samir Datta, Sambuddha Roy","doi":"10.1109/CCC.2006.22","DOIUrl":"https://doi.org/10.1109/CCC.2006.22","url":null,"abstract":"We study the complexity of reachability problems on various classes of grid graphs. Reachability on certain classes of grid graphs gives natural examples of problems that are hard for NC1 under AC0 reductions but are not known to be hard far L; they thus give insight into the structure of L. In addition to explicating the structure of L, another of our goals is to expand the class of digraphs for which connectivity can be solved in logspace, by building on the work of Jakoby et al. (2001), who showed that reachability in series-parallel digraphs is solvable in L. We show that reachability for single-source multiple sink planar dags is solvable in L","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"26 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":"128116737","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: 25
Hardness of the covering radius problem on lattices 格上覆盖半径问题的硬度
21st Annual IEEE Conference on Computational Complexity (CCC'06) Pub Date : 2006-07-16 DOI: 10.1109/CCC.2006.23
I. Haviv, O. Regev
{"title":"Hardness of the covering radius problem on lattices","authors":"I. Haviv, O. Regev","doi":"10.1109/CCC.2006.23","DOIUrl":"https://doi.org/10.1109/CCC.2006.23","url":null,"abstract":"We provide the first hardness result for the covering radius problem on lattices (CRP). Namely, we show that for any large enough p les infin there exists a constant cp > 1 such that CRP in the lscrp norm is Pi2-hard to approximate to within any constant less than cp. In particular, for the case p = infin, we obtain the constant Cinfin = 1.5. This gets close to the constant 2 beyond which the problem is not believed to be Pi2-hard. As part of our proof, we establish a stronger hardness of approximation result for the forallexist-3-SAT problem with bounded occurrences. This hardness result might be useful elsewhere","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"23 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":"114792324","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: 27
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信