Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)最新文献
{"title":"Proofs, codes, and polynomial-time reducibilities","authors":"Ravi Kumar, D. Sivakumar","doi":"10.1109/CCC.1999.766261","DOIUrl":"https://doi.org/10.1109/CCC.1999.766261","url":null,"abstract":"We show how to construct proof systems for NP languages where a deterministic polynomial-time verifier can check membership, given any N/sup (2/3)+/spl epsi// bits of an N-bit witness of membership. We also provide a slightly superpolynomial time proof system where the verifier can check membership, given only N/sup (1/2)+/spl epsi// bits of an N-bit witness. These pursuits are motivated by the work of Gal et. al. (1997). In addition, we construct proof systems where a deterministic polynomial-time verifier can check membership, given an N-bit string that agrees with a legitimate witness on just (N/2)+N/sup (4/5)+/spl epsi// bits. Our results and framework have applications for two related areas of research in complexity theory: proof systems for NP, and the relative power of Cook reductions and Karp-Levin type reductions. Our proof techniques are based on algebraic coding theory and small sample space constructions.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117353679","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}
A. Muchnik, Andrei E. Romashchenko, A. Shen, N. Vereshchagin
{"title":"Upper semilattice of binary strings with the relation \"x is simple conditional to y\"","authors":"A. Muchnik, Andrei E. Romashchenko, A. Shen, N. Vereshchagin","doi":"10.1109/CCC.1999.766270","DOIUrl":"https://doi.org/10.1109/CCC.1999.766270","url":null,"abstract":"In this paper we construct a structure R that is a \"finite version\" of the semilattice of Turing degrees. Its elements are strings (technically, sequences of strings) and x/spl les/y means that K(x|)=(conditional Kolmogorov complexity of x relative to y) is small. We construct two elements in R that do not have greatest lower bound. We give a series of examples that show how natural algebraic constructions give two elements that have lower bound O (minimal element) but significant mutual information. (A first example of that kind was constructed by Gacs-Korner (1973) using completely different technique.) We define a notion of \"complexity profile\" of the pair of elements of R and give (exact) upper and lower bounds for it in a particular case.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128517107","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":"Deterministic amplification of space-bounded probabilistic algorithms","authors":"Ziv Bar-Yossef, Oded Goldreich, A. Wigderson","doi":"10.1109/CCC.1999.766276","DOIUrl":"https://doi.org/10.1109/CCC.1999.766276","url":null,"abstract":"This paper initiates the study of deterministic amplification of space-bounded probabilistic algorithms. The straightforward implementations of known amplification methods cannot be used for such algorithms, since they consume too much space. We present a new implementation of the Ajtai-Komlos-Szemeredi method, that enables to amplify an S-space algorithm that uses r random bits and errs with probability /spl epsiv/ to an O(kS)-space algorithm that uses r+O(k) random bits and errs with probability /spl epsiv//sup /spl Omega/(k)/. This method can be used to reduce the error probability of BPL algorithms below any constant, with only a constant addition of new random bits. This is weaker than the exponential reduction that can be achieved for BPP algorithms by methods that use only O(r) random bits. However we prove that any black-box amplification method that uses O(r) random bits and makes at most p parallel simulations reduces the error to at most /spl epsiv//sup O(p)/. Hence, in BPL, where p should be a constant, the error cannot be reduced to less than a constant. This means that our method is optimal with respect to black-box amplification methods, that use O(r) random bits. The new implementation of the AKS method is based on explicit constructions of constant-space online extractors and online expanders. These are extractors and expanders, for which neighborhoods can be computed in a constant space by a Turing machine with a one-way input tape.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127764122","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":"Stronger separations for random-self-reducibility, rounds, and advice","authors":"L. Babai, Sophie Laplante","doi":"10.1109/CCC.1999.766268","DOIUrl":"https://doi.org/10.1109/CCC.1999.766268","url":null,"abstract":"A function f is self-reducible if it can be computed given an oracle for f. In a random-self-reduction the queries must be made in such a way that the distribution of the ith query is independent of the input that gave rise to it. Random-self-reductions have many applications, including countless cryptographic protocols, probabilistically checkable proofs, average-case complexity, and program checking. A simpler model of randomized self-reducibility is coherence, in which the only condition on the queries is that the input itself may not be among the queries. We show that there is a function which is random-self-reducible with 2 rounds of queries, but which is not even coherent, even if polynomial advice is allowed, when the queries must be made in a single round.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129190483","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}
D. A. Barrington, Chi-Jen Lu, Peter Bro Miltersen, Sven Skyum
{"title":"On monotone planar circuits","authors":"D. A. Barrington, Chi-Jen Lu, Peter Bro Miltersen, Sven Skyum","doi":"10.1109/CCC.1999.766259","DOIUrl":"https://doi.org/10.1109/CCC.1999.766259","url":null,"abstract":"In this paper we show several results about monotone planar circuits. We show that monotone planar circuits of bounded width, with access to negated input variables, compute exactly the functions in non-uniform AC/sup 0/. This provides a striking contrast to the non-planar case, where exactly NC/sup 1/ is computed. We show that the circuit value problem for monotone planar circuits, with inputs on the outerface only, can be solved in LOGDCFL/spl sube/SC, improving a LOGCFL upper bound due to Dymond and Cook. We show that for monotone planar circuits, with inputs on the outerface only, excessive depth compared to width is useless; any function computed by a monotone planar circuit of width w with inputs on the outerface can be computed by a monotone planar circuit of width O(w) and depth w/sup O(1)/. Finally, we show that monotone planar read-once circuits, with inputs on the outerface only, can be efficiently learned using membership queries.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"06 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128729078","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 recent progress on the complexity of lattice problems","authors":"Jin-Yi Cai","doi":"10.1109/CCC.1999.766274","DOIUrl":"https://doi.org/10.1109/CCC.1999.766274","url":null,"abstract":"We survey some recent developments in the study of the complexity of lattice problems. After a discussion of some problems on lattices which can be algorithmically solved efficiently, our main focus is the recent progress on complexity results of intractability. We discuss Ajtai's worst-case/average-case connections, NP-hardness and non-NP-hardness, transference theorems between primal and dual lattices, and the Ajtai-Dwork cryptosystem.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133698679","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":"Applications of a new transference theorem to Ajtai's connection factor","authors":"Jin-Yi Cai","doi":"10.1109/CCC.1999.766278","DOIUrl":"https://doi.org/10.1109/CCC.1999.766278","url":null,"abstract":"We apply a new transference theorem from the geometry of numbers to Ajtai's connection of average-case to worst-case complexity of lattice problems. We also derive stronger bounds for the special class of lattices which possess n/sup /spl epsiv//-unique shortest lattice vectors. This class of lattices plays a significant role in Ajtai's connection of average-case to worst-case complexity of the shortest lattice vector problem, and in the Ajtai-Dwork public-key cryptosystem. Our proofs are non-constructive, based on methods from harmonic analysis. They yield currently the best Ajtai connection factors.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"3 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123873428","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":"Query order and NP-completeness","authors":"J. J. Dai, J. H. Lutz","doi":"10.1109/CCC.1999.766272","DOIUrl":"https://doi.org/10.1109/CCC.1999.766272","url":null,"abstract":"The effect of query order on NP-completeness is investigated. A sequence D/spl I.oarr/=(D/sub 1/,...,D/sub k/) of decision problems is defined to be sequentially complete for NP if each D/sub i//spl isin/NP and every problem in NP can be decided in polynomial time with one query to each of D/sub 1/,...,D/sub k/ in this order. It is shown that, if NP contains a language that is p-generic in the sense of Ambos-Spies, Fleischhack, and Huwig (1987), then for every integer k/spl ges/2, there is a sequence D/spl I.oarr/=(d/sub 1/,...,D/sub k/) such that D is sequentially complete for NP, but no nontrivial permutation (D(i/sub 1/),...,D(i/sub k/)) of D/spl I.oarr/ is sequentially complete for NP. It follows that such a sequence D/spl I.oarr/ exists if there is any strongly positive, p-computable probability measure /spl nu/ such that \"/sub p/(NP)/spl ne/0.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128830356","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":"Learning DNF by approximating inclusion-exclusion formulae","authors":"J. Tarui, Tatsuie Tsukiji","doi":"10.1109/CCC.1999.766279","DOIUrl":"https://doi.org/10.1109/CCC.1999.766279","url":null,"abstract":"We analyze upper and lower bounds on size of Boolean conjunctions necessary and sufficient to approximate a given DNF formula by accuracy slightly better than 1/2 (here we define the size of a Boolean conjunction as the number of distinct variables on which it depends). Such an analysis determines the performance of a naive search algorithm that exhausts Boolean conjunctions in the order of their sizes. In fact, our analysis does not depend on kinds of symmetric functions to be exhausted: instead of conjunctions, counting either disjunctions, parity functions, majority functions, or even general symmetric functions, derives the same learning results from similar analyses.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129111972","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":"A lower bound for primality","authors":"E. Allender, M. Saks, I. Shparlinski","doi":"10.1109/CCC.1999.766257","DOIUrl":"https://doi.org/10.1109/CCC.1999.766257","url":null,"abstract":"Recent work by Bernasconi, Damm and Shparlinski proved lower bounds on the circuit complexity of the square-free numbers, and raised as an open question if similar (or stronger) lower bounds could be proved for the set of prime numbers. In this short note, we answer this question affirmatively, by showing that the set of prime numbers (represented in the usual binary notation) is not contained in AC/sup 0/ [p] for any prime p. Similar lower bounds are presented for the set of square-free numbers, and for the problem of computing the greatest common divisor of two numbers.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114667840","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}