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[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference最新文献

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Complexity classes and sparse oracles 复杂性类和稀疏预言机
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160248
D. P. Bovet, P. Crescenzi, R. Silvestri
{"title":"Complexity classes and sparse oracles","authors":"D. P. Bovet, P. Crescenzi, R. Silvestri","doi":"10.1109/SCT.1991.160248","DOIUrl":"https://doi.org/10.1109/SCT.1991.160248","url":null,"abstract":"The authors obtain positive relativization results. In particular, the goal is to prove statements of the kind: 'Given two complexity classes C/sub 1/ and C/sub 2/, C/sub 1/=C/sub 2/ if and only if for every sparse set S, C/sub 1//sup S/=C/sub 2//sup S/.' The authors derive a sufficient condition to obtain such results and, as an application, they prove a general theorem from which, as far as they know, all of the results obtained previously along with new ones can be immediately derived.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"351 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134115860","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: 33
The perceptron strikes back 感知器会反击
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160270
R. Beigel, N. Reingold, D. Spielman
{"title":"The perceptron strikes back","authors":"R. Beigel, N. Reingold, D. Spielman","doi":"10.1109/SCT.1991.160270","DOIUrl":"https://doi.org/10.1109/SCT.1991.160270","url":null,"abstract":"It is shown that every AC/sup 0/ predicate is computed by a low-degree probabilistic polynomial over the reals. It is demonstrated that circuits composed of a symmetric gate at the root with AND-OR subcircuits of constant depth can be simulated by probabilistic depth-2 circuits with essentially the same symmetric gate at the root and AND gates of small fanin at the bottom. In particular, every language recognized by a depth-d AC/sup 0/ circuit is decidable by a probabilistic perceptron of size 2 to the power O(log/sup 4d/ n) and of order O(log/sup 4d/ n) that uses O(log/sup 3/ n) probabilistic bits. As a corollary, the authors present a new proof that depth-d AND-OR circuits computing the parity of n binary inputs require size 2 to the power n/sup Omega (1/d)/.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127760030","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: 73
Counting classes are at least as hard as the polynomial-time hierarchy 计数类至少和多项式时间层次结构一样困难
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160238
Seinosuke Toda, M. Ogihara
{"title":"Counting classes are at least as hard as the polynomial-time hierarchy","authors":"Seinosuke Toda, M. Ogihara","doi":"10.1109/SCT.1991.160238","DOIUrl":"https://doi.org/10.1109/SCT.1991.160238","url":null,"abstract":"It is shown that many natural counting classes are at least as computationally hard as PH (the polynomial-time hierarchy) in the following sense: for each K of the counting classes, every set in K(PH) is polynomial-time randomized many-one reducible to a set in K with two-sided exponentially small error probability. As a consequence, these counting classes are computationally harder than PH unless PH collapses to a finite level. Some other consequences are also shown.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114666150","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: 151
On the success probability of the two provers in one-round proof systems 关于一轮证明系统中两个证明者的成功概率
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160251
U. Feige
{"title":"On the success probability of the two provers in one-round proof systems","authors":"U. Feige","doi":"10.1109/SCT.1991.160251","DOIUrl":"https://doi.org/10.1109/SCT.1991.160251","url":null,"abstract":"The author addresses the problem of reducing the error probability of two-prover one-round proof systems, without increasing the number of provers or the number of rounds. An example, the noninteractive agreement protocol, where executing such a protocol twice in parallel does not decrease the error probability at all is constructed. Upper bounds on the error probability of specific classes of protocols are proved. As a corollary, it is shown that every NEXPTIME language has a one-round two-prover proof system with constant error probability.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129677391","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: 92
Adaptive logspace and depth-bounded reducibilities 自适应对数空间和深度界可约性
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160267
J. Balcázar
{"title":"Adaptive logspace and depth-bounded reducibilities","authors":"J. Balcázar","doi":"10.1109/SCT.1991.160267","DOIUrl":"https://doi.org/10.1109/SCT.1991.160267","url":null,"abstract":"The author discusses a number of results regarding the study of the computational power of depth-bounded reducibilities, their use to classify the complexity of computational problems, and their characterizations in terms of other computational models. In particular, problems arising in the design of concurrent systems are studied, and two kinds of logarithmic space reductions are defined. The first one is nonadaptive and equivalent in many respects to the oracle set model. The second provides a notion of adaptive logspace reducibility which turns out to characterize precisely depth-bounded reductions. The closures of NP under these reducibilities are also treated.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125896012","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: 6
On the Monte Carlo Boolean decision tree complexity of read-once formulae 关于蒙特卡罗布尔决策树一次读公式的复杂度
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160259
M. Santha
{"title":"On the Monte Carlo Boolean decision tree complexity of read-once formulae","authors":"M. Santha","doi":"10.1109/SCT.1991.160259","DOIUrl":"https://doi.org/10.1109/SCT.1991.160259","url":null,"abstract":"In the Boolean decision tree model there is at least a linear gap between the Monte Carlo and the Las Vegas complexity of a function depending on the error probability. The author proves for a large class of read-once formulae that this trivial speed-up is the best that a Monte Carlo algorithm can achieve. For every formula F belonging to that class it is shown that the Monte Carlo complexity of F with two-sided error p is (1-2p)R(F), and with one-sided error p is (1-p)R(F), where R(F) denotes the Las Vegas complexity of F. The result follows from a general lower bound that is derived on the Monte Carlo complexity of these formulae.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123484174","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: 64
The power of witness reduction 证人减刑的力量
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160242
Sanjay Gupta
{"title":"The power of witness reduction","authors":"Sanjay Gupta","doi":"10.1109/SCT.1991.160242","DOIUrl":"https://doi.org/10.1109/SCT.1991.160242","url":null,"abstract":"Recent results by M. Ogiwara and L.A. Hemachandra (1990) established a connection between functions being hard for a class of functions and functions interacting with the class to effect witness reduction. The author believes that the ability to achieve some form of witness reduction is what makes a function hard for a class of functions. To support this thesis he defines new function classes and obtains results analogous to those of Ogiwara and Hemachandra. He also introduces the notion of randomly hard functions and obtains similar results.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122262505","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: 22
Lower bounds with smaller domain size on concurrent write parallel machines 并发写并行机上较小域大小的下界
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160276
J. Edmonds
{"title":"Lower bounds with smaller domain size on concurrent write parallel machines","authors":"J. Edmonds","doi":"10.1109/SCT.1991.160276","DOIUrl":"https://doi.org/10.1109/SCT.1991.160276","url":null,"abstract":"The author proves an optimum lower bound, separating the PRIORITY and the COMMON PRAM models on a much more reasonably sized input domain than that shown by R.B. Boppana (1989). The proposed techniques provide a greater understanding of the partial information a processor learns about the input. For example, the author defines a new measure of the dependency that a function has on a variable and develops new set theoretic techniques to replace the use of Ramsey theory (which had forced the domain size to be large).<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128416963","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
Notions of resource-bounded category and genericity 资源有界范畴和一般性的概念
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160262
Stephen A. Fenner
{"title":"Notions of resource-bounded category and genericity","authors":"Stephen A. Fenner","doi":"10.1109/SCT.1991.160262","DOIUrl":"https://doi.org/10.1109/SCT.1991.160262","url":null,"abstract":"The author investigates the strength of resource-bounded generic sets for deciding results in relativized complexity. He makes technical improvements to J.H. Lutz's notion of resource-bounded Baire category (1987, 1989) to show that almost every exponential-time set (in the author's sense of category) separate P from NP. It is shown that the author's improved notion of category, while strictly more powerful, still has all the other desirable properties of Lutz's characterization of resource-bounded category in terms of Banach-Mazur games. He then considers the amount of genericity needed to prove result of M. Blum and R. Impagliazzo (1987) regarding NP intersection co-NP and one-way functions. It is found that although these results hold for 1-generic sets, they cannot be guaranteed even by extremely powerful but slightly weaker generics. A crucial difference between 1-genericity and weaker notions is thus isolated. The author studies this weaker notion of genericity and shows that it has recursion-theoretic properties radically different from 1-genericity.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134520088","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: 26
Geometric arguments yield better bounds for threshold circuits and distributed computing 几何参数为阈值电路和分布式计算提供了更好的边界
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160275
Matthias Krause
{"title":"Geometric arguments yield better bounds for threshold circuits and distributed computing","authors":"Matthias Krause","doi":"10.1109/SCT.1991.160275","DOIUrl":"https://doi.org/10.1109/SCT.1991.160275","url":null,"abstract":"The computational power of two-party probabilistic communication protocols is investigated. This model generalizes the concepts of nondeterministic and conondeterministic communication protocols in a natural way. Applications of the technique are presented, and some open problems are stated.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115746878","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: 49
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