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

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A stronger Kolmogorov zero-one law for resource-bounded measure 资源有限测度的更强Kolmogorov 0 - 1定律
Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933887
J. J. Dai
{"title":"A stronger Kolmogorov zero-one law for resource-bounded measure","authors":"J. J. Dai","doi":"10.1109/CCC.2001.933887","DOIUrl":"https://doi.org/10.1109/CCC.2001.933887","url":null,"abstract":"Resource-bounded measure has been defined on the classes E, E/sub 2/, ESPACE, E/sub 2/SPACE, REC, and the class of all languages. It is shown here that if C is any of these classes and X is a set of languages that is closed under finite variations and has outer measure less than 1 in C, then X has measure 0 in C. This result strengthens Lutz's resource-bounded generalization of the classical Kolmogorov zero-one law. It also gives a useful sufficient condition for proving that a set has measure 0 in a complexity class.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"16 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":"121525620","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: 3
Links between complexity theory and constrained block coding 复杂性理论与约束分组编码之间的联系
Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933890
L. Stockmeyer, D. Modha
{"title":"Links between complexity theory and constrained block coding","authors":"L. Stockmeyer, D. Modha","doi":"10.1109/CCC.2001.933890","DOIUrl":"https://doi.org/10.1109/CCC.2001.933890","url":null,"abstract":"The goal of this paper is to establish links between computational complexity theory and the theory and practice of constrained block coding. The complexities of several fundamental problems in constrained block coding are shown to be complete in various classes of the existing complexity-theoretic structure. The results include (relatively rare) /spl Sigma//sub 2//sup p/-, /spl Sigma//sub 3//sup p/, and NP/sup PP/-completeness results. Two types of problems are considered: (1) the problem of designing encoder and decoder circuits using minimum or approximately minimum hardware for a given constraint and a given rate; (2) computing the maximum rate of a block code for a given constraint and codeword length. In both cases, a constraint is specified by a deterministic finite state transition diagram. Another question studied is whether maximum-rate block codes can always be implemented by encoders and decoders of polynomial size. The answer to this question is shown to be closely related to the complexity of PP.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"29 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":"128477081","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: 3
Computational depth 计算深度
Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI: 10.1109/CCC.2001.933893
L. Antunes, L. Fortnow, D. Melkebeek
{"title":"Computational depth","authors":"L. Antunes, L. Fortnow, D. Melkebeek","doi":"10.1109/CCC.2001.933893","DOIUrl":"https://doi.org/10.1109/CCC.2001.933893","url":null,"abstract":"Introduces computational depth, a measure for the amount of \"non-random\" or \"useful\" information in a string, by considering the difference of various Kolmogorov complexity measures. We investigate three instantiations of computational depth: (1) basic computational depth, a clean notion capturing the spirit of C.H. Bennett's (1988) logical depth; (2) time-t computational depth and the resulting concept of shallow sets, a generalization of sparse and random sets based on low depth properties of their characteristic sequences (we show that every computable set that is reducible to a shallow set has polynomial-size circuits); and (3) distinguishing computational depth, measuring when strings are easier to recognize than to produce (we show that if a Boolean formula has a non-negligible fraction of its satisfying assignments with low depth, then we can find a satisfying assignment efficiently).","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"185 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":"121522829","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
Quantum algorithmic entropy 量子算法熵
Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2000-11-12 DOI: 10.1109/CCC.2001.933894
P. Gács
{"title":"Quantum algorithmic entropy","authors":"P. Gács","doi":"10.1109/CCC.2001.933894","DOIUrl":"https://doi.org/10.1109/CCC.2001.933894","url":null,"abstract":"Extends algorithmic information theory to quantum mechanics, taking a universal semi-computable density matrix (\"universal probability\") as a starting point, and defines complexity (an operator) as its negative logarithm. A number of properties of Kolmogorov complexity extend naturally to the new domain. Approximately, a quantum state is simple if it is within a small distance from a low-dimensional subspace of low Kolmogorov complexity. The von-Neumann entropy of a computable density matrix is within an additive constant from the average complexity. Some of the theory of randomness translates to the new domain. We explore the relations of the new quantity to the quantum Kolmogorov complexity defined by P.M.B. Vita/spl acute/nyi (1999) (we show that the latter is sometimes as large as 2n-2 log n) and the qubit complexity defined by A. Berthiaume et al. (2000). The \"cloning\" properties of our complexity measure are similar to those of qubit complexity.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128730505","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: 83
Quantum versus classical learnability 量子与经典易学性
Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2000-07-12 DOI: 10.1109/CCC.2001.933881
R. Servedio, S. Gortler
{"title":"Quantum versus classical learnability","authors":"R. Servedio, S. Gortler","doi":"10.1109/CCC.2001.933881","DOIUrl":"https://doi.org/10.1109/CCC.2001.933881","url":null,"abstract":"Motivated by work on quantum black-box query complexity, we consider quantum versions of two well-studied models of learning Boolean functions: Angluin's (1988) model of exact learning from membership queries and Valiant's (1984) Probably Approximately Correct (PAC) model of learning from random examples. For each of these two learning models we establish a polynomial relationship between the number of quantum versus classical queries required for learning. Our results provide an interesting contrast to known results which show that testing black-box functions for various properties can require exponentially more classical queries than quantum queries. We also show that under a widely held computational hardness assumption there is a class of Boolean functions which is polynomial-time learnable in the quantum version but not the classical version of each learning model; thus while quantum and classical learning are equally powerful from an information theory perspective, they are different when viewed from a computational complexity perspective.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132481219","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: 30
Quantum algorithms for element distinctness 元素独特性的量子算法
Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2000-07-06 DOI: 10.1137/S0097539702402780
H. Buhrman, C. Dürr, M. Heiligman, P. Høyer, F. Magniez, M. Santha, R. D. Wolf
{"title":"Quantum algorithms for element distinctness","authors":"H. Buhrman, C. Dürr, M. Heiligman, P. Høyer, F. Magniez, M. Santha, R. D. Wolf","doi":"10.1137/S0097539702402780","DOIUrl":"https://doi.org/10.1137/S0097539702402780","url":null,"abstract":"We present several applications of quantum amplitude amplification to finding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard, Hoyer, and Tapp (1998), and imply an O(N/sup 3/4/ log N) quantum upper bound for the element distinctness problem in the comparison complexity model. This contrasts with /spl Theta/(N log N) classical complexity. We also prove a lower bound of /spl Omega/(/spl radic/N) comparisons for this problem and derive bounds for a number of related problems.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122260359","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
Communication complexity lower bounds by polynomials 多项式的通信复杂度下界
Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 1999-10-12 DOI: 10.1109/CCC.2001.933879
H. Buhrman, R. D. Wolf
{"title":"Communication complexity lower bounds by polynomials","authors":"H. Buhrman, R. D. Wolf","doi":"10.1109/CCC.2001.933879","DOIUrl":"https://doi.org/10.1109/CCC.2001.933879","url":null,"abstract":"The quantum version of communication complexity allows the two communicating parties to exchange qubits and/or to make use of prior entanglement (shared EPR-pairs). Some lower bound techniques are available for qubit communication complexity, but except for the inner product function, no bounds are known for the model with unlimited prior entanglement. We show that the \"log rank\" lower bound extends to the strongest variant of quantum communication complexity (qubit communication+unlimited prior entanglement). By relating the rank of the communication matrix to properties of polynomials, we are able to derive some strong bounds for exact protocols. In particular, we prove both the \"log rank conjecture\" and the polynomial equivalence of quantum and classical communication complexity for various classes of functions. We also derive some weaker bounds for bounded-error quantum protocols.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114464487","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: 134
Monotone simulations of nonmonotone proofs 非单调证明的单调模拟
Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 1900-01-01 DOI: 10.1109/CCC.2001.933870
Albert Atserias, Nicola Galesi, P. Pudlák
{"title":"Monotone simulations of nonmonotone proofs","authors":"Albert Atserias, Nicola Galesi, P. Pudlák","doi":"10.1109/CCC.2001.933870","DOIUrl":"https://doi.org/10.1109/CCC.2001.933870","url":null,"abstract":"We show that an LK proof of size m of a monotone sequent (a sequent that contains only formulas in the basis /spl and/, V) can be turned into a proof containing only monotone formulas of size m/sup O(log m)/ and with the number of proof lines polynomial in m. Also we show that some interesting special cases, namely the functional and the onto versions of PHP and a version of the matching principle, have polynomial size monotone proofs.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"74 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":"124647567","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: 16
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