Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.最新文献

{"title":"Solvable group isomorphism is (almost) in NP /spl cap/ CoNP","authors":"V. Arvind, J. Torán","doi":"10.1145/1944857.1944859","DOIUrl":"https://doi.org/10.1145/1944857.1944859","url":null,"abstract":"The group isomorphism problem consists in deciding whether two input groups G/sup 1/ and G/sup 2/ given by their multiplication tables are isomorphic. We first give a 2-round Arthur-Merlin protocol for the group non-isomorphism problem such that on input groups (G/sup 1/, G/sup 2/) of size n, Arthur uses O(log/sup 6/ n) random bits and Merlin uses O(log/sup 2/ n) nondeterministic bits. We derandomize this protocol for the case of solvable groups showing the following two results: (a) We give a uniform NP machine for solvable group non-isomorphism, that works correctly on all but 2/sup polylog(n)/ inputs of any length n. Furthermore, this NP machine is always correct when the input groups are nonisomorphic. The NP machine is obtained by an unconditional derandomization of the AM protocol. (b) Under the assumption that EXP /spl nsube/ i.o.PSPACE we get a complete derandomization of the above AM protocol. Thus, EXP /spl nsube/ i.o.PSPACE implies that group isomorphism for solvable groups is in NP /spl cap/ coNP.","PeriodicalId":430345,"journal":{"name":"Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.","volume":"20 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132285660","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}

{"title":"The complexity of the covering radius problem on lattices and codes","authors":"V. Guruswami, Daniele Micciancio, O. Regev","doi":"10.1109/CCC.2004.1313831","DOIUrl":"https://doi.org/10.1109/CCC.2004.1313831","url":null,"abstract":"We initiate the study of the computational complexity of the covering radius problem for point lattices, and approximation versions of the problem for both lattices and linear codes. We also investigate the computational complexity of the shortest linearly independent vectors problem, and its relation to the covering radius problem for lattices. For the covering radius on n-dimensional lattices, we show that the problem can be approximated within any constant factor /spl gamma/(n) > 1 in random exponential time 2/sup O(n)/, it is in AM for /spl gamma/(n) = 2, in coAM for /spl gamma/(n) = /spl radic/(n log n), and in NP /spl cap/ coNP for /spl gamma/(n) = /spl radic/n. For the covering radius on n-dimensional linear codes, we show that the problem can be solved in deterministic polynomial time for approximation factor /spl gamma/(n) = log n, but cannot be solved in polynomial time for some /spl gamma/(n) = /spl Omega/(log log n) unless NP can be simulated in deterministic n/sup O(log log log n)/ time. Moreover, we prove that the problem is NP-hard for every constant approximation factor, it is /spl Pi//sub 2/-hard for some constant approximation factor, and it is in AM for approximation factor 2. So, it is unlikely to be /spl Pi//sub 2/-hard for approximation factors larger than 2. This is a natural hardness of approximation result in the polynomial hierarchy. For the shortest independent vectors problem, we give a coAM protocol achieving approximation factor /spl gamma/(n) = /spl radic/(n/log n), solving an open problem of Blomer and Seifert (1999), and prove that the problem is also in coNP for /spl gamma/(n) = /spl radic/n. Both results are obtained by giving a gap-preserving nondeterministic polynomial time reduction to the closest vector problem.","PeriodicalId":430345,"journal":{"name":"Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127662073","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}

{"title":"Tight lower bounds for certain parameterized NP-hard problems","authors":"Jianer Chen, B. Chor, M. Fellows, Xiuzhen Huang, D. Juedes, Iyad A. Kanj, Ge Xia","doi":"10.1109/CCC.2004.1313826","DOIUrl":"https://doi.org/10.1109/CCC.2004.1313826","url":null,"abstract":"Based on the framework of parameterized complexity theory, we derive tight lower bounds on the computational complexity for a number of well-known NP-hard problems. We start by proving a general result, namely that the parameterized weighted satisfiability problem on depth-t circuits cannot be solved in time n/sup o(k)/poly(m), where n is the circuit input length, m is the circuit size, and k is the parameter, unless the (t - l)-st level W[t $1] of the W-hierarchy collapses to FPT. By refining this technique, we prove that a group of parameterized NP-hard problems, including weighted SAT, dominating set, hitting set, set cover, and feature set, cannot be solved in time n/sup o(k)/poly(m), where n is the size of the universal set from which the k elements are to be selected and m is the instance size, unless the first level W[l] of the W-hierarchy collapses to FPT. We also prove that another group of parameterized problems which includes weighted q-SAT (for any fixed q /spl ges/ 2), clique, and independent set, cannot be solved in time n/sup o(k)/ unless all search problems in the syntactic class SNP, introduced by Papadimitriou and Yannakakis, are solvable in subexponential time. Note that all these parameterized problems have trivial algorithms of running time either n/sup k/ poly(m) or O(n/sup k/).","PeriodicalId":430345,"journal":{"name":"Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114352044","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}

{"title":"The complexity of treelike systems over /spl lambda/-local formulae","authors":"Nicola Galesi, Neil Thapen","doi":"10.1109/CCC.2004.1313798","DOIUrl":"https://doi.org/10.1109/CCC.2004.1313798","url":null,"abstract":"We describe a system LK(c[/spl lambda/]) for refuting CNF formulae, as a restriction of the sequent calculus in which every formula in a sequent is defined over at most /spl lambda/ variables. This further generalizes the system Res(k), a generalization of Resolution to k-DNF introduced in (Krajicek, 2001). We adapt the Pudlak-Impagliazzo game (Pudlak and Impagliazzo, 2000) to prove lower bounds for treelike LK(c[/spl lambda/]). We show that dynamic satisfiability, which was introduced in (Esteban et al., 2002) to study resolution space complexity, is a sufficient \"but not necessary\" condition to obtain exponential lower bounds.","PeriodicalId":430345,"journal":{"name":"Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130991588","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}

{"title":"Properties of NP-complete sets","authors":"Christian Glaßer, A. Pavan, A. Selman, Samik Sengupta","doi":"10.1137/S009753970444421X","DOIUrl":"https://doi.org/10.1137/S009753970444421X","url":null,"abstract":"We study several properties of sets that are complete for NP. We prove that if L is an NP-complete set and S /spl nsupe/ L is a p-selective sparse set, then L -S is /spl les//sub m//sup p/-hard for NP. We demonstrate existence of a sparse set S /spl isin/ DTIME(2/sup 2n/) such that for every L /spl isin/ NP - P, L - S is not /spl les//sub m//sup p/-hard for NP. Moreover, we prove for every L /spl isin/ NP - P, that there exists a sparse S /spl isin/ EXP such that L - S is not /spl les//sub m//sup p/-hard for NP. Hence, removing sparse information in P from a complete set leaves the set complete, while removing sparse information in EXP from a complete set may destroy its completeness. Previously, these properties were known only for exponential time complexity classes. We use hypotheses about pseudorandom generators and secure one-way permutations to derive consequences for long-standing open questions about whether NP-complete sets are immune. For example, assuming that pseudorandom generators and secure one-way permutations exist, it follows easily that NP-complete sets are not p-immune. Assuming only that secure one-way permutations exist, we prove that no NP-complete set is DTIME(2/sup ne/)-immune. Also, using these hypotheses we show that no NP-complete set is quasipolynomial-close to P. We introduce a strong but reasonable hypothesis and infer from it that disjoint Turing-complete sets for NP are not closed under union. Our hypothesis asserts existence of a UP-machine M that accepts 0* such that for some 0 < /spl epsi/ < 1, no 2/sup ne/ time-bounded machine can correctly compute infinitely many accepting computations of M, We show that if UP /spl cap/ coUP contains DTIME(2/sup ne/)-bi-immune sets, then this hypothesis is true.","PeriodicalId":430345,"journal":{"name":"Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.","volume":"263 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132220944","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}

{"title":"Lower bounds for testing bipartiteness in dense graphs","authors":"Andrej Bogdanov, L. Trevisan","doi":"10.1109/CCC.2004.1313803","DOIUrl":"https://doi.org/10.1109/CCC.2004.1313803","url":null,"abstract":"We consider the problem of testing bipartiteness in the adjacency matrix model. The best known algorithm, due to Alon and Krivelevich, distinguishes between bipartite graphs and graphs that are /spl epsi/-far from bipartite using 0(1//spl epsi//sup 2/) queries. We show that this is optimal for non-adaptive algorithms, up to polylogarithmic factors. We also show a lower bound of /spl Omega/(1//spl epsi//sup 3/2/) for adaptive algorithms.","PeriodicalId":430345,"journal":{"name":"Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130460861","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}

{"title":"Abelian permutation group problems and logspace counting classes","authors":"V. Arvind, T. Vijayaraghavan","doi":"10.1109/CCC.2004.1313844","DOIUrl":"https://doi.org/10.1109/CCC.2004.1313844","url":null,"abstract":"The goal of this paper is to classify abelian permutation group problems using logspace counting classes. Building on McKenzie and Cook's [MC87] classification of permutation group problems into four NC Turing-equivalent sets, we show that all these problems are essentially captured by the generalized logspace mod-class ModL, where ModL is the logspace analogue of ModP (defined by Kobler and Toda (KT96)). More precisely, our results are as follows: 1. For abelian permutation groups, the problems of membership testing, isomorphism testing and computing the order of a group are all in ZPL/sup ModL/, and are all hard for ModL under logspace Turing reductions. 2. The problems of computing the intersection of abelian permutation groups, and computing a generator-relator presentation for a given abelian permutation group are in FL/sup ModL//poly. Furthermore, the search version of membership testing is also in FL/sup ModL//poly.","PeriodicalId":430345,"journal":{"name":"Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.","volume":"129 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114001659","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}

{"title":"On pseudoentropy versus compressibility","authors":"H. Wee","doi":"10.1109/CCC.2004.1313782","DOIUrl":"https://doi.org/10.1109/CCC.2004.1313782","url":null,"abstract":"A source is comprehensible if we can efficiently compute short descriptions of strings in the support and efficiently recover the strings from the descriptions. A source has high pseudo-entropy if it is computationally distinguishable from a source of high entropy. In this paper, we present a technique for proving lower bounds on compressibility in an oracle setting, which yields the following results: 1. We exhibit oracles relative to which there exists samplable sources over {0, 1}/sup n/ of low pseudoentropy (say n/2) that cannot be compressed to length less than n - /spl omega/(log n) by polynomial size circuits. This matches the upper bounds in (Goldberg and Sipser, 1991, Trevisan et al., 2004), and provides an oracle separation between compressibility and pseudoentropy, thereby partially addressing an open problem posed in (Impagliazzo, 1999). 2. We also provide a separation between 1/s-metric-type pseudoentropy and 1/s-Yao-type pseudoentropy - which are two computational analogues of entropy introduced in (Barak et al., 2003) - for the class of oracle circuits of sizes (s polynomially bounded). This is the first known separation result for metric-type and Yao-type pseudoentropy. 3. In the random oracle model, we show that there exists in compressible functions as defined in (Dwork et al., 1996) where any substantial compression of the output of the function must reveal something about the seed. This yields the first known practical realization of incompressible functions, under the assumption that random oracles may be realized using cryptographic hash functions. Finally, we show that computational assumptions are needed to separate compressibility and pseudoentropy for samplable sources. In particular, if one-way functions do not exist, then any samplable flat source of entropy k can be compressed by circuits to length k + 0(log n); furthermore, any such source has 1/2-Yao-type pseudoentropy k + 0(log n).","PeriodicalId":430345,"journal":{"name":"Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131243687","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}

{"title":"Some results on majority quantifiers over words","authors":"Klaus-Jörn Lange","doi":"10.1109/CCC.2004.1313817","DOIUrl":"https://doi.org/10.1109/CCC.2004.1313817","url":null,"abstract":"The class of languages definable by majority quantifiers using the order predicate is investigated. It is shown that the additional use of first order or counting quantifiers does not increase this class. Further on, addition is in this connection a definable numerical predicate, while the converse does not hold. The emptiness problem for this class turns out to be undecidable.","PeriodicalId":430345,"journal":{"name":"Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131099932","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}

{"title":"On the power of quantum proofs","authors":"R. Raz, Amir Shpilka","doi":"10.1109/CCC.2004.1313849","DOIUrl":"https://doi.org/10.1109/CCC.2004.1313849","url":null,"abstract":"We study the power of quantum proofs, or more precisely, the power of quantum Merlin-Arthur (QMA) protocols, in two well studied models of quantum computation: the black box model and the communication complexity model. Our main results are obtained for the communication complexity model. For this model, we identify a complete promise problem for QMA protocols, the linear sub-spaces distance problem. The problem is of geometrical nature: each player gets a linear subspace of R/sup m/ and considers the sphere of unit vectors in that subspace. Their goal is to output 1 if the distance between the two spheres is very small (say, smaller than 0.1 /spl middot/ /spl radic/2) and 0 if the distance is very large (say, larger than 0.9 /spl middot/ /spl radic/2). We show that: 1. The QMA communication complexity of the problem is O(logm). 2. The (classical) MA communication complexity of the problem is /spl Omega/(m/sup /spl epsi//) (for some /spl epsi/ > 0). 3. The (standard) quantum communication complexity of the problem is /spl Omega/(/spl radic/m). In particular, this gives an exponential separation between QMA communication complexity and MA communication complexity. For the black box model we give several observations. First, we observe that the block sensitivity method, as well as the polynomial method for proving lower bounds for the number of queries, can both be extended to QMA protocols. We use these methods to obtain lower bounds for the QMA black box complexity of functions. In particular, we obtain a tight lower bound of /spl Omega/(N) for the QMA black box complexity of a random function, and a tight lower bound of /spl Omega/(/spl radic/N) for the QMA black box query complexity of NOR(X/sub 1/,..., X/sub n/). In particular, this shows that any attempt to give short quantum proofs for the class of languages Co - NP have to go beyond black box arguments. We also observe that for any Boolean function G(X/sub 1/,..., X/sub n/), if for both G and 7minus;G there are QMA black box protocols that make at most T queries to the black box, then there is a classical deterministic black box protocol for G that makes 0(T/sup 6/) queries to the black box. In particular, this shows that in the black box model QMA /spl cap/ Co - QMA = P. On the positive side, we observe that any (total or partial) Boolean function G(X/sub 1/,..., X/sub n/) has a QMA black box protocol with proofs of length N that makes only 0(/spl radic/N) queries to the black box. Finally, we observe a very simple proof for the exponential separation (for promise problems) between QMA black box complexity and (classical) MA black box complexity (first obtained by Watrous).","PeriodicalId":430345,"journal":{"name":"Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.","volume":"43 20","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132389814","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}