Proceedings 16th Annual IEEE Conference on Computational Complexity最新文献_第2页

Resolution complexity of independent sets in random graphs 随机图中独立集的解析复杂度

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933872

P. Beame, R. Impagliazzo, Ashish Sabharwal

引用次数: 6

Space complexity of random formulae in resolution 分辨率中随机公式的空间复杂度

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933871

Eli Ben-Sasson, Nicola Galesi

{"title":"Space complexity of random formulae in resolution","authors":"Eli Ben-Sasson, Nicola Galesi","doi":"10.1109/CCC.2001.933871","DOIUrl":"https://doi.org/10.1109/CCC.2001.933871","url":null,"abstract":"We study the space complexity of refuting unsatisfiable random k-CNFs in the resolution proof system. We prove that for any large enough /spl Delta/, with high probability a random k-CNF over n variables and /spl Delta/n clauses requires resolution clause space of /spl Omega/(n/spl middot//spl Delta//sup -1+/spl epsiv//k-2-/spl epsiv//), for any 0</spl epsiv/<1/2. For constant /spl Delta/, this gives us linear, optimal, lower bounds on the clause space. A nice consequence of this lower bound is the first lower bound for size of tree-like resolution refutations of random 3-CNFs with clause density /spl Delta/>>/spl radic/n. This bound is nearly tight. Specifically, we show that with high probability, a random 3-CNF with /spl Delta/n clauses requires tree-like refutation size of exp(/spl Omega/(n//spl Delta//sup 1+/spl epsiv//1-/spl epsiv//)), for any 0</spl epsiv/<1/2. Our space lower bound is the consequence of three main contributions. 1. We introduce a 2-player matching game on bipartite graphs G to prove that there are no perfect matchings in G. 2. We reduce lower bounds for the clause space of a formula F in resolution to lower bounds for the complexity of the game played on the bipartite graph G(F) associated with F. 3. We prove that the complexity of the game is large whenever G is an expander graph. Finally, a simple probabilistic analysis shows that for a random formula F, with high probability G(F) is an expander. We also extend our result to the case of G-PHP, a generalization of the pigeonhole principle based on bipartite graphs G. We prove that the clause space for G-PHP can be reduced to the game complexity on G.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"13 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":"131049294","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: 87

Comparing notions of full derandomization 比较完全非随机化的概念

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933869

L. Fortnow

引用次数: 23

Tree resolution proofs of the weak pigeon-hole principle 弱鸽子洞原理的树分辨率证明

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933873

Stefan S. Dantchev, Søren Riis

引用次数: 24

Universal traversal sequences with backtracking 带回溯的通用遍历序列

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933868

M. Koucký

引用次数: 64

Time-space tradeoffs in the counting hierarchy 计数层次结构中的时空权衡

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933896

E. Allender, M. Koucký, Detlef Ronneburger, Sambuddha Roy, V. Vinay

引用次数: 30

Simple analysis of graph tests for linearity and PCP 线性和PCP的图形检验的简单分析

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933891

J. Håstad, A. Wigderson

引用次数: 90

Towards uniform AC/sup 0/-isomorphisms 趋于一致AC/sup 0/-同构

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933866

Manindra Agrawal

引用次数: 1

In search of an easy witness: exponential time vs. probabilistic polynomial time 寻找一个简单的证明:指数时间vs.概率多项式时间

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933865

R. Impagliazzo, Valentine Kabanets, A. Wigderson

引用次数: 225

On the non-approximability of Boolean functions by OBDDs and read-k-times branching programs 用obdd和读k次分支程序研究布尔函数的非逼近性

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933884

Beate Bollig, Martin Sauerhoff, I. Wegener

{"title":"On the non-approximability of Boolean functions by OBDDs and read-k-times branching programs","authors":"Beate Bollig, Martin Sauerhoff, I. Wegener","doi":"10.1109/CCC.2001.933884","DOIUrl":"https://doi.org/10.1109/CCC.2001.933884","url":null,"abstract":"Branching problems are considered as a nonuniform model of computation in complexity theory as well as a data structure for boolean functions in several applications. In many applications (e.g., verification), exact representations are required. For learning boolean functions f on the basis of classified examples, it is sufficient to produce the representation of a function g approximating f. This motivates the investigation of the size of the smallest branching program approximating f. Although several non-approximability results are contained in the papers on randomized branching programs, these results often do not work for the uniform distribution (which is the most important one in applications). Here, the following non-approximability results are presented. (1) It is proven that a simple function from the branching program literature requires exponential size to be approximated with respect to the uniform distribution by OBDDs, which are the most important type of branching programs in applications. (2) The first truly exponential lower bound on the size of approximating syntactic read-k-times branching programs with respect to the uniform distribution and error probability 1/2-2/sup -/spl Omega/(n)/, n the input size, is shown. In order to improve upon the so far best results for error probabilities smaller than 1/3, a strong combinatorial lemma from a recent paper of Ajtai on linear-length branching programs is exploited.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"213 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":"127783646","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: 8