Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)最新文献

Efficient Arguments without Short PCPs 没有简短pcp的有效论证

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1109/CCC.2007.10

Y. Ishai, E. Kushilevitz, R. Ostrovsky

{"title":"Efficient Arguments without Short PCPs","authors":"Y. Ishai, E. Kushilevitz, R. Ostrovsky","doi":"10.1109/CCC.2007.10","DOIUrl":"https://doi.org/10.1109/CCC.2007.10","url":null,"abstract":"Current constructions of efficient argument systems combine a short (polynomial size) PCP with a cryptographic hashing technique. We suggest an alternative approach for this problem that allows to simplify the underlying PCP machinery using a stronger cryptographic technique. More concretely, we present a direct method for compiling an exponentially long PCP which is succinctly described by a linear oracle function pi : F^n to F into an argument system in which the verifier sends to the prover O(n) encrypted field elements and receives O(1) encryptions in return. This compiler can be based on an arbitrary homomorphic encryption scheme. Applying our general compiler to the exponential size Hadamard code based PCP of Arora et al. (JACM 1998) yields a simple argument system for NP in which the communication from the prover to the verifier only includes a constant number of short encryptions. The main tool we use is a new cryptographic primitive which allows to efficiently commit to a linear function and later open the output of the function on an arbitrary vector. Our efficient implementation of this primitive is independently motivated by cryptographic applications.","PeriodicalId":175854,"journal":{"name":"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131990137","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: 129

On Heuristic Time Hierarchies 启发式时间层次

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1109/CCC.2007.20

Konstantin Pervyshev

引用次数: 14

Testing Properties of Constraint-Graphs 约束图的性质测试

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1109/CCC.2007.31

S. Halevy, Oded Lachish, I. Newman, Dekel Tsur

{"title":"Testing Properties of Constraint-Graphs","authors":"S. Halevy, Oded Lachish, I. Newman, Dekel Tsur","doi":"10.1109/CCC.2007.31","DOIUrl":"https://doi.org/10.1109/CCC.2007.31","url":null,"abstract":"We study a model of graph related formulae that we call the constraint-graph model. A constraint-graph is a labeled multi-graph (a graph where loops and parallel edges are allowed), where each edge e is labeled by a distinct Boolean variable and every vertex is associated with a Boolean function over the variables that label its adjacent edges. A Boolean assignment to the variables satisfies the constraint graph if it satisfies every vertex function. We associate with a constraint-graph G the property that consists of all assignments satisfying G, denoted SAT(G). We show that the above model is quite general. That is, for every property of strings P there exists a property of constraint-graphs PG such that P is testable using q queries if and only if PG is thus testable. In addition, we present a large family of constraint-graphs for which SAT(G) is testable with constant number of queries. As an implication of this, we infer the testability of some edge coloring problems (e.g. the property of two coloring of the edges in which every node is adjacent to at least one vertex of each color). Another implication is that every property of Boolean strings that can be represented by a read-twice CNF formula is testable. We note that this is the best possible in terms of the number of occurrences of every variable in a formula.","PeriodicalId":175854,"journal":{"name":"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114405925","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

Understanding Parallel Repetition Requires Understanding Foams 理解平行重复需要理解泡沫

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1109/CCC.2007.39

U. Feige, Guy Kindler, R. O'Donnell

引用次数: 60

The Complexity of Polynomials and Their Coefficient Functions 多项式及其系数函数的复杂性

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1109/CCC.2007.33

Guillaume Malod

引用次数: 21

On Computation and Communication with Small Bias 小偏差下的计算与通信

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1007/978-3-540-74871-7_1

H. Buhrman

引用次数: 110

Unbalanced Expanders and Randomness Extractors from Parvaresh-Vardy Codes Parvaresh-Vardy码的不平衡扩展器和随机提取器

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1145/1538902.1538904

V. Guruswami, C. Umans, Salil P. Vadhan

{"title":"Unbalanced Expanders and Randomness Extractors from Parvaresh-Vardy Codes","authors":"V. Guruswami, C. Umans, Salil P. Vadhan","doi":"10.1145/1538902.1538904","DOIUrl":"https://doi.org/10.1145/1538902.1538904","url":null,"abstract":"We give an improved explicit construction of highly unbalanced bipartite expander graphs with expansion arbitrarily close to the degree (which is polylogarithmic in the number of vertices). Both the degree and the number of right-hand vertices are polynomially close to optimal, whereas the previous constructions of Ta-Shma, Umans, and Zuckerman (STOC \"01) required at least one of these to be quasipolynomial in the optimal. Our expanders have a short and self-contained description and analysis, based on the ideas underlying the recent list-decodable error-correcting codes of Parvaresh and Vardy (FOCS \"05). Our expanders can be interpreted as near-optimal \"randomness condensers,\" that reduce the task of extracting randomness from sources of arbitrary min-entropy rate to extracting randomness from sources of min-entropy rate arbitrarily close to 1, which is a much easier task. Using this connection, we obtain a new construction of randomness extractors that is optimal up to constant factors, while being much simpler than the previous construction of Lu et al. (STOC \"03) and improving upon it when the error parameter is small (e.g. 1/poly(n)).","PeriodicalId":175854,"journal":{"name":"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129105801","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: 423

On C-Degrees, H-Degrees and T-Degrees c度，h度和t度

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1109/CCC.2007.17

W. Merkle, F. Stephan

{"title":"On C-Degrees, H-Degrees and T-Degrees","authors":"W. Merkle, F. Stephan","doi":"10.1109/CCC.2007.17","DOIUrl":"https://doi.org/10.1109/CCC.2007.17","url":null,"abstract":"Following a line of research that aims at relating the computation power and the initial segment complexity of a set, the work presented here investigates into the relations between Turing reducibility, defined in terms of computation power, and C-reducibility and H-reducibility, defined in terms of the complexity of initial segments. The global structures of all C-degrees and of all H-degrees are rich and allows to embed the lattice of the powerset of the natural numbers under inclusion. In particular, there are C-degrees, as well as H-degrees, that are different from the least degree and are the meet of two other degrees, whereas on the other hand there are pairs of sets that have a meet neither in the C-degrees nor in the H-degrees; these results answer questions in a survey by Nies and Miller. There are r.e. sets that form a minimal pair for C-reducibility and Sigma2 0 sets that form a minimal pair for H-reducibility, which answers questions by Downey and Hirschfeldt. Furthermore, the following facts on the relation between C-degrees, H-degrees and Turing degrees hold. Every C-degree contains at most one Turing degree and this bound is sharp since there are C-degrees that do contain a Turing degree. For the comprising class of complex sets, neither the C-degree nor the H-degree of such a set can contain a Turing degree, in fact, the Turing degree of any complex set contains infinitely many C-degrees. Similarly the Turing degree of any set that computes the halting problem contains infinitely many H-degrees, while the H-degree of any 2-random set R is never contained in the Turing degree of R. By the latter, H-equivalence of Martin-Lof random sets does not imply their Turing equivalence. The structure of the Cdegrees contained in the Turing degree of a complex sets is rich and allows to embed any countable distributive lattice; a corresponding statement is true for the structure of H-degrees that are contained in the Turing degree of a set that computes the halting problem.","PeriodicalId":175854,"journal":{"name":"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)","volume":"370 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125724814","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

Parity Problems in Planar Graphs 平面图中的宇称问题

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1109/CCC.2007.23

M. Braverman, R. Kulkarni, Sambuddha Roy

引用次数: 8

Bounded Queries and the NP Machine Hypothesis 有界查询与NP机假设

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1109/CCC.2007.7

Richard Chang, Suresh Purini

引用次数: 4