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Proceedings 17th IEEE Annual Conference on Computational Complexity最新文献

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Pseudo-random generators for all hardnesses 所有硬度的伪随机生成器
Proceedings 17th IEEE Annual Conference on Computational Complexity Pub Date : 2002-05-19 DOI: 10.1145/509907.509997
C. Umans
{"title":"Pseudo-random generators for all hardnesses","authors":"C. Umans","doi":"10.1145/509907.509997","DOIUrl":"https://doi.org/10.1145/509907.509997","url":null,"abstract":"(MATH) We construct the first pseudo-random generators with logarithmic seed length that convert s bits of hardness into sΩ(1) bits of 2-sided pseudo-randomness for any s}. This improves [8] and gives a direct proof of the optimal hardness vs. randomness tradeoff in [15]. A key element in our construction is an augmentation of the standard low-degree extension encoding that exploits the field structure of the underlying space in a new way.","PeriodicalId":193513,"journal":{"name":"Proceedings 17th IEEE Annual Conference on Computational Complexity","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128248004","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: 131
Extracting quantum entanglement (general entanglement purification protocols) 提取量子纠缠(一般纠缠净化协议)
Proceedings 17th IEEE Annual Conference on Computational Complexity Pub Date : 2001-10-01 DOI: 10.1109/CCC.2002.1004345
A. Ambainis, Adam D. Smith, Ke Yang
{"title":"Extracting quantum entanglement (general entanglement purification protocols)","authors":"A. Ambainis, Adam D. Smith, Ke Yang","doi":"10.1109/CCC.2002.1004345","DOIUrl":"https://doi.org/10.1109/CCC.2002.1004345","url":null,"abstract":"We study the problem of extracting Einstein-Podolsky-Rosen (EPR) pairs from a general source of entanglement. Suppose Alice and Bob share a bipartite state /spl rho/ which is \"reasonably close\" to perfect EPR pairs. The only information Alice and Bob possess is a lower bound on the fidelity of /spl rho/ and a maximally entangled state. They wish to \"purify\" /spl rho/ using local operations and classical communication, and output a state that is arbitrarily close to EPR pairs. We prove that, on average, Alice and Bob cannot increase the fidelity of the input state significantly. On the other hand, there exist protocols that may fail with a small probability, and otherwise will output states arbitrarily close to EPR pairs with very high probability. These protocols come from the \"purity-testing protocols\" of H. Barnum et al. (2001).","PeriodicalId":193513,"journal":{"name":"Proceedings 17th IEEE Annual Conference on Computational Complexity","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116197145","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: 15
Algebras of minimal rank over perfect fields 完备域上最小秩代数
Proceedings 17th IEEE Annual Conference on Computational Complexity Pub Date : 1900-01-01 DOI: 10.1109/CCC.2002.1004346
M. Blaser
{"title":"Algebras of minimal rank over perfect fields","authors":"M. Blaser","doi":"10.1109/CCC.2002.1004346","DOIUrl":"https://doi.org/10.1109/CCC.2002.1004346","url":null,"abstract":"Let R(A) denote the rank (also called the bilinear complexity) of a finite-dimensional associative algebra A. A fundamental lower bound for R(A) is the so-called Alder-Strassen (1981) bound: R(A) /spl ges/ 2 dim A-t, where t is the number of maximal two-sided ideals of A. The class of algebras for which the Alder-Strassen bound is sharp, the so-called \"algebras of minimal rank\", has received wide attention in algebraic complexity theory. We characterize all algebras of minimal rank over perfect fields. This solves an open problem in algebraic complexity theory over perfect fields [as discussed by V. Strassen (1990) and P. Bu/spl uml/rgisser et al. (1997)]. As a by-product, we determine all algebras A of minimal rank with A/rad A /spl cong/ k/sup t/ over arbitrary fields.","PeriodicalId":193513,"journal":{"name":"Proceedings 17th IEEE Annual Conference on Computational Complexity","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114481494","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: 2
Hard examples for bounded depth Frege 有界深度弗雷格的硬例子
Proceedings 17th IEEE Annual Conference on Computational Complexity Pub Date : 1900-01-01 DOI: 10.1109/CCC.2002.1004323
Eli Ben-Sasson
{"title":"Hard examples for bounded depth Frege","authors":"Eli Ben-Sasson","doi":"10.1109/CCC.2002.1004323","DOIUrl":"https://doi.org/10.1109/CCC.2002.1004323","url":null,"abstract":"We prove exponential lower bounds on the size of a bounded depth Frege proof of a Tseitin graph-based contradiction, whenever the underlying graph is an expander. This is the first example of a contradiction, naturally formalized as a 3-CNF, that has no short bounded depth Frege proofs.","PeriodicalId":193513,"journal":{"name":"Proceedings 17th IEEE Annual Conference on Computational Complexity","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127383777","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: 0
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