18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.最新文献

Holographic proofs and derandomization 全息证明和非随机化

18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings. Pub Date : 2003-07-07 DOI: 10.1109/CCC.2003.1214427

D. Melkebeek, R. Santhanam

{"title":"Holographic proofs and derandomization","authors":"D. Melkebeek, R. Santhanam","doi":"10.1109/CCC.2003.1214427","DOIUrl":"https://doi.org/10.1109/CCC.2003.1214427","url":null,"abstract":"We derive a stronger consequence of EXP having polynomial-size circuits than was known previously, namely that there is a simulation of P in MAPOLYLOG that fools all deterministic polynomial-time adversaries. Using the connection between circuit lower bounds and derandomization, we obtain uniform assumptions for derandomizing BPP. Our results strengthen the space-randomness tradeoffs of Sipser, Nisan and Wigderson, and Lu. We show a partial converse: oracle circuit lower bounds for EXP imply that there are efficient simulations of P that fool deterministic polynomial-time adversaries. We also consider a more quantitative notion of simulation, where the measure of success of the simulation is the fraction of inputs of a given length on which the simulation works. Among other results, we show that if there is no polynomial time bound t such that P can be simulated well by MATIME(t), then for any /spl epsi/>0 there is a simulation of BPP in P that works for all but 2/sup n/spl epsi// inputs of length n. This is a uniform strengthening of a recent result of Goldreich and Wigderson. Finally, we give an unconditional simulation of multitape Turing machines operating in probabilistic time t by Turing machines operating in deterministic time O(2/sup t/). We show similar results for randomized NC/sup 1/ circuits. Our proofs are based on a combination of techniques in the theory of derandomization with results on holographic proofs.","PeriodicalId":286846,"journal":{"name":"18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.","volume":"205 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122502736","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: 13

Near-optimal lower bounds on the multi-party communication complexity of set disjointness 集不连通下多方通信复杂度的近最优下界

18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings. Pub Date : 2003-07-07 DOI: 10.1109/CCC.2003.1214414

Amit Chakrabarti, Subhash Khot, Xiaodong Sun

{"title":"Near-optimal lower bounds on the multi-party communication complexity of set disjointness","authors":"Amit Chakrabarti, Subhash Khot, Xiaodong Sun","doi":"10.1109/CCC.2003.1214414","DOIUrl":"https://doi.org/10.1109/CCC.2003.1214414","url":null,"abstract":"We study the communication complexity of the set disjointness problem in the general multiparty model. For t players, each holding a subset of a universe of size n, we establish a near-optimal lower bound of /spl Omega/(n/(t log t)) on the communication complexity of the problem of determining whether their sets are disjoint. In the more restrictive one-way communication model, in which the players are required to speak in a predetermined order, we improve our bound to an optimal /spl Omega/(n/t). These results improve upon the earlier bounds of /spl Omega/(n/t/sup 2/) in the general model, and /spl Omega/((/spl epsiv//sup 2/n)/t/sup 1+/spl epsiv//) in the one-way model, due to Bar-Yossef, Jayram, Kumar, and Sivakumar (2002). As in the case of earlier results, our bounds apply to the unique intersection promise problem. This communication problem is known to have connections with the space complexity of approximating frequency moments in the data stream model. Our results lead to an improved space complexity lower bound of /spl Omega/(n/sup 1-2/k//log n) for approximating the k/sup th/ frequency moment with a constant number of passes over the input, and a technical improvement to /spl Omega/(n/sup 1-2/k/) if only one pass over the input is permitted. Our proofs rely on the information theoretic direct sum decomposition paradigm of Bar-Yossef et al. [2002]. Our improvements stem from novel analytical techniques, as opposed to earlier techniques based on Hellinger and related distances, for estimating the information cost of protocols for one-bit functions.","PeriodicalId":286846,"journal":{"name":"18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128738603","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: 201

Derandomization and distinguishing complexity 非随机化和区分复杂性

18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings. Pub Date : 2003-07-07 DOI: 10.1109/CCC.2003.1214421

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

{"title":"Derandomization and distinguishing complexity","authors":"E. Allender, M. Koucký, Detlef Ronneburger, Sambuddha Roy","doi":"10.1109/CCC.2003.1214421","DOIUrl":"https://doi.org/10.1109/CCC.2003.1214421","url":null,"abstract":"We continue an investigation of resource-bounded Kolmogorov complexity and derandomization techniques begun in [E. Allender (2001), E. Allender et al., (2002)]. We introduce nondeterministic time-bounded Kolmogorov complexity measures (KNt and KNT) and examine the properties of these measures using constructions of hitting set generators for nondeterministic circuits [P. B. Miltersen et al., (1999), R. Shaltiel et al., (2001)]. We observe that KNt bears many similarities to the nondeterministic distinguishing complexity CND of [H. Buhrman et al., (2002)]. This motivates the definition of a new notion of time-bounded distinguishing complexity KDt, as an intermediate notion with connections to the class FewEXP. The set of KDt-random strings is complete for EXP under P/poly reductions. Most of the notions of resource-bounded Kolmogorov complexity discussed here and in [E. Allender (2001), E. Allender et al., (2002)] have close connections to circuit size (on different types of circuits). We extend this framework to define notions of Kolmogorov complexity KB and KF that are related to branching program size and formula size, respectively. The sets of KB- and KF-random strings lie in coNP; we show that oracle access to these sets enables one to factor Blum integers. We obtain related intractability results for approximating minimum formula size, branching program size, and circuit size. The NEXP/spl sube/NC and NEXP/spl sube/L/poly questions are shown to be equivalent to conditions about the KF and KB complexity of sets in P.","PeriodicalId":286846,"journal":{"name":"18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125883618","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

On statistical query sampling and NMR quantum computing 统计查询采样和核磁共振量子计算

18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings. Pub Date : 2003-07-07 DOI: 10.1109/CCC.2003.1214420

Ke Yang, Avrim Blum

{"title":"On statistical query sampling and NMR quantum computing","authors":"Ke Yang, Avrim Blum","doi":"10.1109/CCC.2003.1214420","DOIUrl":"https://doi.org/10.1109/CCC.2003.1214420","url":null,"abstract":"We introduce a \"statistical query sampling\" model, in which the goal of an algorithm is to produce an element in a hidden set S/spl sube/{0,1}/sup n/ with reasonable probability. The algorithm gains information about S through oracle calls (statistical queries), where the algorithm submits a query function g(/spl middot/) and receives an approximation to Pr/sub x/spl isin/S/[g(x)=1]. We show how this model is related to NMR quantum computing, in which only statistical properties of an ensemble of quantum systems can be measured, and in particular to the question of whether one can translate standard quantum algorithms to the NMR setting without putting all of their classical postprocessing into the quantum system. Using Fourier analysis techniques developed in the related context of statistical query learning, we prove a number of lower bounds (both information-theoretic and cryptographic) on the ability of algorithms to produce an x/spl isin/S, even when the set S is fairly simple. These lower bounds point out a difficulty in efficiently applying NMR quantum computing to algorithms such as Shor's and Simon's algorithm that involve significant classical postprocessing. We also explicitly relate the notion of statistical query sampling to that of statistical query learning.","PeriodicalId":286846,"journal":{"name":"18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.","volume":"2009 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125650383","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

List decoding with side information 带副信息的解码列表

18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings. Pub Date : 2003-07-07 DOI: 10.1109/CCC.2003.1214429

V. Guruswami

{"title":"List decoding with side information","authors":"V. Guruswami","doi":"10.1109/CCC.2003.1214429","DOIUrl":"https://doi.org/10.1109/CCC.2003.1214429","url":null,"abstract":"Under list decoding of error-correcting codes, the decoding algorithm is allowed to output a small list of codewords that are close to the noisy received word. This relaxation permits recovery even under very high noise thresholds. We consider one possible scenario that would permit disambiguating between the elements of the list, namely where the sender of the message provides some hopefully small amount of side information about the transmitted message on a separate auxiliary channel that is noise-free. This setting becomes meaningful and useful when the amount of side information that needs to be communicated is much smaller than the length of the message. We study what kind of side information is necessary and sufficient in the above context. The short, conceptual answer is that the side information must be randomized and the message recovery is with a small failure probability. Specifically, we prove that deterministic schemes, which guarantee correct recovery of the message, provide no savings and essentially the entire message has to be sent as side information. However there exist randomized schemes, which only need side information of length logarithmic in the message length. In fact, in the limit of repeated communication of several messages, amortized amount of side information needed per message can be a constant independent of the message length or the failure probability. Concretely, we can correct up to a fraction (1/2-/spl gamma/) of errors for binary codes using only 2log(1//spl gamma/)+O(1) amortized bits of side information per message, and this is in fact the best possible (up to additive constant terms).","PeriodicalId":286846,"journal":{"name":"18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121472920","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: 36

On derandomizing tests for certain polynomial identities 若干多项式恒等式的非随机化检验

18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings. Pub Date : 2003-07-07 DOI: 10.1109/CCC.2003.1214434

Manindra Agrawal

引用次数: 13

Lower bounds for predecessor searching in the cell probe model 单元探针模型中前驱搜索的下界

18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings. Pub Date : 2003-07-07 DOI: 10.1109/CCC.2003.1214411

P. Sen, Venkatesh Srinivasan

{"title":"Lower bounds for predecessor searching in the cell probe model","authors":"P. Sen, Venkatesh Srinivasan","doi":"10.1109/CCC.2003.1214411","DOIUrl":"https://doi.org/10.1109/CCC.2003.1214411","url":null,"abstract":"We consider a fundamental problem in data structures, static predecessor searching: Given a subset S of size n from the universe [m], store S so that queries of the form \"What is the predecessor of x in S?\" can be answered efficiently. We study this problem in the cell probe model introduced by Yao [1981]. Recently, Beame and Fich [2002] obtained optimal bounds on the number of probes needed by any deterministic query scheme if the associated storage scheme uses only n/sup O(1)/ cells of word size (log m)/sup O(1)/ bits. We give a new lower bound proof for this problem that matches the bounds of Beame and Fich. Our lower bound proof has the following advantages: it works for randomised query schemes too, while Beame and Fich's proof works for deterministic query schemes only. In addition, it is simpler than Beame and Fich's proof. We prove our lower bound using the round elimination approach of Miltersen, Nisan, Safra and Wigderson [1998]. Using tools from information theory, we prove a strong round elimination lemma for communication complexity that enables us to obtain a tight lower bound for the predecessor problem. We also use our round elimination lemma to obtain a rounds versus communication tradeoff for the 'greater-than' problem, improving on the tradeoff in [1998]. We believe that our round elimination lemma is of independent interest and should have other applications.","PeriodicalId":286846,"journal":{"name":"18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.","volume":"246 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116442647","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

Minimization of decision trees is hard to approximate 决策树的最小化很难近似

18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings. Pub Date : 2003-07-07 DOI: 10.1109/CCC.2003.1214412

Detlef Sieling

引用次数: 32

Proving SAT does not have small circuits with an application to the two queries problem 通过两个查询问题的应用证明SAT没有小电路

18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings. Pub Date : 2003-07-07 DOI: 10.1109/CCC.2003.1214433

L. Fortnow, A. Pavan, Samik Sengupta

引用次数: 23

Bounded nondeterminism and alternation in parameterized complexity theory 参数化复杂性理论中的有界不确定性与交替

18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings. Pub Date : 2003-07-07 DOI: 10.1109/CCC.2003.1214407

Yijia Chen, J. Flum, Martin Grohe

引用次数: 47