Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)最新文献

The minimum equivalent DNF problem and shortest implicants 最小等效DNF问题和最短隐含问题

Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-11-08 DOI: 10.1109/SFCS.1998.743506

C. Umans

引用次数: 151

Lower bounds for zero knowledge on the Internet 互联网上零知识的下限

Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-11-08 DOI: 10.1109/SFCS.1998.743499

J. Kilian, E. Petrank, C. Rackoff

引用次数: 94

On learning monotone Boolean functions 关于单调布尔函数的学习

Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-11-08 DOI: 10.1109/SFCS.1998.743491

Avrim Blum, C. Burch, J. Langford

引用次数: 53

Randomness vs. time: de-randomization under a uniform assumption 随机vs.时间:统一假设下的去随机化

Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-11-08 DOI: 10.1109/SFCS.1998.743524

R. Impagliazzo, A. Wigderson

{"title":"Randomness vs. time: de-randomization under a uniform assumption","authors":"R. Impagliazzo, A. Wigderson","doi":"10.1109/SFCS.1998.743524","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743524","url":null,"abstract":"We prove that if BPP/spl ne/EXP, then every problem in BPP can be solved deterministically in subexponential time on almost every input (on every samplable ensemble for infinitely many input sizes). This is the first derandomization result for BPP based on uniform, noncryptographic hardness assumptions. It implies the following gap in the average-instance complexities of problems in BPP: either these complexities are always sub-exponential or they contain arbitrarily large exponential functions. We use a construction of a small \"pseudorandom\" set of strings from a \"hard function\" in EXP which is identical to that used in the analogous non-uniform results described previously. However, previous proofs of correctness assume the \"hard function\" is not in P/poly. They give a non-constructive argument that a circuit distinguishing the pseudo-random strings from truly random strings implies that a similarly-sized circuit exists computing the \"hard function\". Our main technical contribution is to show that, if the \"hard function\" has certain properties, then this argument can be made constructive. We then show that, assuming ESP/spl sube/P/poly, there are EXP-complete functions with these properties.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"2001 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128294362","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: 183

Lower bounds for (MOD p-MOD m) circuits (MOD p-MOD m)电路的下界

Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-11-08 DOI: 10.1109/SFCS.1998.743459

V. Grolmusz, G. Tardos

引用次数: 23

Unsatisfiable systems of equations, over a finite field 有限域上的不可满足方程组

Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-11-08 DOI: 10.1109/SFCS.1998.743444

Alan R. Woods

引用次数: 6

Exponential complexity lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields 有限域上函数代数中深度3算术电路的指数复杂度下界

Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-11-08 DOI: 10.1109/SFCS.1998.743456

D. Grigoriev, A. Razborov

引用次数: 36

Improved decoding of Reed-Solomon and algebraic-geometric codes 里德-所罗门码和代数-几何码的改进解码

Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-11-08 DOI: 10.1109/SFCS.1998.743426

V. Guruswami, M. Sudan

{"title":"Improved decoding of Reed-Solomon and algebraic-geometric codes","authors":"V. Guruswami, M. Sudan","doi":"10.1109/SFCS.1998.743426","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743426","url":null,"abstract":"Given an error-correcting code over strings of length n and an arbitrary input string also of length n, the list decoding problem is that of finding all codewords within a specified Hamming distance from the input string. We present an improved list decoding algorithm for decoding Reed-Solomon codes. The list decoding problem for Reed-Solomon codes reduces to the following \"curve-fitting\" problem over a field F: Given n points {(x/sub i/.y/sub i/)}/sub i=1//sup n/, x/sub i/,y/sub i//spl isin/F, and a degree parameter k and error parameter e, find all univariate polynomials p of degree at most k such that y/sub i/=p(x/sub i/) for all but at most e values of i/spl isin/{1....,n}. We give an algorithm that solves this problem for e1/3, where the result yields the first asymptotic improvement in four decades. The algorithm generalizes to solve the list decoding problem for other algebraic codes, specifically alternant codes (a class of codes including BCH codes) and algebraic-geometric codes. In both cases, we obtain a list decoding algorithm that corrects up to n-/spl radic/(n-d-) errors, where n is the block length and d' is the designed distance of the code. The improvement for the case of algebraic-geometric codes extends the methods of Shokrollahi and Wasserman (1998) and improves upon their bound for every choice of n and d'. We also present some other consequences of our algorithm including a solution to a weighted curve fitting problem, which is of use in soft-decision decoding algorithms for Reed-Solomon codes.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"157 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134064670","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: 1226

The complexity of acyclic conjunctive queries 非循环连接查询的复杂性

Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-11-08 DOI: 10.1109/SFCS.1998.743521

G. Gottlob, N. Leone, Francesco Scarcello

引用次数: 3

A unified superfast algorithm for boundary rational tangential interpolation problems and for inversion and factorization of dense structured matrices 边界有理切向插值问题和密集结构矩阵的反演与分解的统一超高速算法

Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) Pub Date : 1998-11-08 DOI: 10.1109/SFCS.1998.743443

V. Olshevsky, V. Pan

{"title":"A unified superfast algorithm for boundary rational tangential interpolation problems and for inversion and factorization of dense structured matrices","authors":"V. Olshevsky, V. Pan","doi":"10.1109/SFCS.1998.743443","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743443","url":null,"abstract":"The classical scalar Nevanlinna-Pick interpolation problem has a long and distinguished history, appearing in a variety of applications in mathematics and electrical engineering. There is a vast literature on this problem and on its various far reaching generalizations. It is widely known that the now classical algorithm for solving this problem proposed by Nevanlinna in 1929 can be seen as a way of computing the Cholesky factorization for the corresponding Pick matrix. Moreover; the classical Nevanlinna algorithm takes advantage of the special structure of the Pick matrix to compute this triangular factorization in only O(n/sup 2/) arithmetic operations, where n is the number of interpolation points, or equivalently, the size of the Pick matrix. Since the structure-ignoring standard Cholesky algorithm [though applicable to the wider class of general matrices] has much higher complexity O(n/sup 3/), the Nevanlinna algorithm is an example of what is now called fast algorithms. In this paper we use a divide-and-conquer approach to propose a new superfast O(n log/sup 3/ n) algorithm to construct solutions for the more general boundary tangential Nevanlinna-Pick problem. This dramatic speed-up is achieved via a new divide-and-conquer algorithm for factorization of rational matrix functions; this superfast algorithm seems to have a practical and theoretical significance itself. It can be used to solve similar rational interpolation problems [e.g., the matrix Nehari problem], and a variety, of engineering problems. It can also be used for inversion and triangular factorization of matrices with displacement structure, including Hankel-like, Vandermonde-like, and Cauchy-like matrices.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130202949","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: 46