Proceedings 16th Annual IEEE Conference on Computational Complexity最新文献

Bounded query functions with limited output bits 具有有限输出位的有限查询函数

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933876

Richard Chang, J. Squire

引用次数: 1

Logical operations and Kolmogorov complexity. II 逻辑运算和柯尔莫哥洛夫复杂度。2

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933892

A. Muchnik, N. Vereshchagin

引用次数: 12

Separation of NP-completeness notions np完备性概念的分离

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933875

A. Pavan, A. Selman

引用次数: 25

Affine projections of symmetric polynomials 对称多项式的仿射投影

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933883

Amir Shpilka

{"title":"Affine projections of symmetric polynomials","authors":"Amir Shpilka","doi":"10.1109/CCC.2001.933883","DOIUrl":"https://doi.org/10.1109/CCC.2001.933883","url":null,"abstract":"We introduce a new model for computing polynomials-a depth 2 circuit with a symmetric gate at the top and plus gates at the bottom, i.e. the circuit computes a symmetric function in linear functions-S/sub m//sup d/(l/sub 1/, l/sub 2/, ..., l/sub m/) (S/sub m//sup d/ is the d'th elementary symmetric polynomial in m variables, and the l/sub i/'s are linear functions). We refer to this model as the symmetric model. This new model is related to standard models of arithmetic circuits, especially to depth 3 circuits. In particular we show that, in order to improve the results of Shpilka and Wigderson (1999), i.e. to prove super-quadratic lower bounds for depth 3 circuits, one must first prove a super-linear lower bound for the symmetric model. We prove two nontrivial linear lower bounds for our model. The first lower bound is for computing the determinant, and the second is for computing the sum of two monomials. The main technical contribution relates the maximal dimension of linear subspaces on which S/sub m//sup d/ vanishes, and lower bounds to the symmetric model. In particular we show that an answer of the following problem (which is very natural, and of independent interest) will imply lower bounds on symmetric circuits for many polynomials: \"what is the maximal dimension of a linear subspace of C/sup m/, on which S/sub m//sup d/ vanishes?\" We give two partial solutions to the problem above, each enables us to prove a different lower bound.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134113134","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: 34

A linear lower bound on the unbounded error probabilistic communication complexity 无界误差概率通信复杂度的线性下界

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933877

J. Forster

引用次数: 208

On the complexity of approximating the VC dimension 关于VC维近似的复杂度

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933889

Elchanan Mossel, C. Umans

引用次数: 46

On the power of nonlinear secret-sharing 关于非线性秘密共享的力量

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933886

A. Beimel, Y. Ishai

{"title":"On the power of nonlinear secret-sharing","authors":"A. Beimel, Y. Ishai","doi":"10.1109/CCC.2001.933886","DOIUrl":"https://doi.org/10.1109/CCC.2001.933886","url":null,"abstract":"A secret-sharing scheme enables a dealer to distribute a secret among no parties such that only some predefined authorized sets of parties will be able to reconstruct the secret from their shares. The (monotone) collection of authorized sets is called an access structure, and is freely identified with its characteristic monotone function f: {0, 1}/sup n//spl rarr/{0, 1}. A family of secret-sharing schemes is called efficient if the total length of the n shares is polynomial in n. Most previously known secret-sharing schemes belonged to a class of linear schemes, whose complexity coincides with the monotone span program size of their access structure. Prior to this work there was no evidence that nonlinear schemes can be significantly more efficient than linear schemes, and in particular there were no candidates for schemes efficiently realizing access structures which do not lie in NC. The main contribution of this work is the construction of two efficient nonlinear schemes: (1) A scheme with perfect privacy whose access structure is conjectured not to lie in NC; (2) A scheme with statistical privacy whose access structure is conjectured not to lie to P/poly. Another contribution is the study of a class of nonlinear schemes, termed quasi-linear schemes, obtained by composing linear schemes over different fields. We show that while these schemes are possibly (super-polynomially) more powerful than linear schemes, they cannot efficiently realize access structures outside NC.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133800142","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: 61

Hausdorff dimension in exponential time 指数时间下的豪斯多夫维数

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933888

K. Ambos-Spies, W. Merkle, Jan Reimann, F. Stephan

引用次数: 38

Lower bounds for approximations by low degree polynomials over Z/sub m/ Z/下标m/上的低次多项式近似的下界

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933885

N. Alon, R. Beigel

引用次数: 42

On separators, segregators and time versus space 关于分隔器，分隔器和时间与空间

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933895

R. Santhanam

{"title":"On separators, segregators and time versus space","authors":"R. Santhanam","doi":"10.1109/CCC.2001.933895","DOIUrl":"https://doi.org/10.1109/CCC.2001.933895","url":null,"abstract":"Gives an extension of the result due to Paul, Pippenger, Szemeredi and Trotter (1983) that deterministic linear time (DTIME) is distinct from nondeterministic linear time (NTIME). We show that NTIME[n/spl radic/log*(n)] /spl ne/ DTIME[n/spl radic/log*(n)]. We show that if the class of multi-pushdown graphs has {o(n), o[n/log(n)]} segregators, then NTIME[n log(n)] /spl ne/ DTIME[n log(n)]. We also show that at least one of the following facts holds: (1) P /spl ne/ L, and (2) for all polynomially bounded constructible time bounds t, NTIME(t) /spl ne/ DTIME(t). We consider the problem of whether NTIME(t) is distinct from NSPACE(t) for constructible time bounds t. A pebble game on graphs is defined such that the existence of a \"good\" strategy for the pebble game on multi-pushdown graphs implies a \"good\" simulation of nondeterministic time-bounded machines by nondeterministic space-bounded machines. It is shown that there exists a \"good\" strategy for the pebble game on multi-pushdown graphs if the graphs have sublinear separators. Finally, we show that nondeterministic time-bounded Turing machines can be simulated by /spl Sigma//sub 4/ machines with an asymptotically smaller time bound, under the assumption that the class of multi-pushdown graphs has sublinear separators.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127314528","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