Results 1  10
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72
Monotone Complexity
, 1990
"... We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a simple ..."
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Cited by 2350 (12 self)
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We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a simple notion of monotone reducibility and exhibit complete problems. This provides a framework for stating existing results and asking new questions. We show that mNL (monotone nondeterministic logspace) is not closed under complementation, in contrast to Immerman's and Szelepcs 'enyi's nonmonotone result [Imm88, Sze87] that NL = coNL; this is a simple extension of the monotone circuit depth lower bound of Karchmer and Wigderson [KW90] for stconnectivity. We also consider mBWBP (monotone bounded width branching programs) and study the question of whether mBWBP is properly contained in mNC 1 , motivated by Barrington's result [Bar89] that BWBP = NC 1 . Although we cannot answer t...
The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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Cited by 188 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
The Load, Capacity and Availability of Quorum Systems
, 1998
"... A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication and dissemination of information Given a strategy to pick quorums, the load L(S) is th ..."
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Cited by 89 (12 self)
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A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication and dissemination of information Given a strategy to pick quorums, the load L(S) is the minimal access probability of the busiest element, minimizing over the strategies. The capacity Cap(S) is the highest quorum accesses rate that S can handle, so Cap(S) = 1=L(S).
Oracles and Queries that are Sufficient for Exact Learning
 Journal of Computer and System Sciences
, 1996
"... We show that the class of all circuits is exactly learnable in randomized expected polynomial time using weak subset and weak superset queries. This is a consequence of the following result which we consider to be of independent interest: circuits are exactly learnable in randomized expected poly ..."
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Cited by 83 (5 self)
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We show that the class of all circuits is exactly learnable in randomized expected polynomial time using weak subset and weak superset queries. This is a consequence of the following result which we consider to be of independent interest: circuits are exactly learnable in randomized expected polynomial time with equivalence queries and the aid of an NPoracle. We also show that circuits are exactly learnable in deterministic polynomial time with equivalence queries and a \Sigma 3 oracle. The hypothesis class for the above learning algorithms is the class of circuits of largerbut polynomially relatedsize. Also, the algorithms can be adapted to learn the class of DNF formulas with hypothesis class consisting of depth3  formulas (by the work of Angluin [A90], this is optimal in the sense that the hypothesis class cannot be reduced to DNF formulas, i.e. depth2  formulas).
Analysis of Random Processes via AndOr Tree Evaluation
 In Proceedings of the 9th Annual ACMSIAM Symposium on Discrete Algorithms
, 1998
"... We introduce a new set of probabilistic analysis tools based on the analysis of AndOr trees with random inputs. These tools provide a unifying, intuitive, and powerful framework for carrying out the analysis of several previously studied random processes of interest, including random lossresilient ..."
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Cited by 73 (23 self)
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We introduce a new set of probabilistic analysis tools based on the analysis of AndOr trees with random inputs. These tools provide a unifying, intuitive, and powerful framework for carrying out the analysis of several previously studied random processes of interest, including random lossresilient codes, solving random kSAT formula using the pure literal rule, and the greedy algorithm for matchings in random graphs. In addition, these tools allow generalizations of these problems not previously analyzed to be analyzed in a straightforward manner. We illustrate our methodology on the three problems listed above. 1 Introduction We introduce a new set of probabilistic analysis tools related to the amplification method introduced by [12] and further developed and used in [13, 5]. These tools provide a unifying, intuitive, and powerful framework for carrying out the analysis of several previously studied random processes of interest, including the random lossresilient codes introduced ...
Lower Bounds for Deterministic and Nondeterministic Branching Programs
 in Proceedings of the FCT'91, Lecture Notes in Computer Science
, 1991
"... We survey lower bounds established for the complexity of computing explicitly given Boolean functions by switchingandrectifier networks, branching programs and switching networks. We first consider the unrestricted case and then proceed to various restricted models. Among these are monotone networ ..."
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Cited by 57 (4 self)
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We survey lower bounds established for the complexity of computing explicitly given Boolean functions by switchingandrectifier networks, branching programs and switching networks. We first consider the unrestricted case and then proceed to various restricted models. Among these are monotone networks, boundedwidth devices , oblivious devices and readk times only devices. 1 Introduction The main goal of the Boolean complexity theory is to prove lower bounds on the complexity of computing "explicitly given" Boolean functions in interesting computational models. By "explicitly given" researchers usually mean "belonging to the class NP ". This is a very plausible interpretation since on the one hand this class contains the overwhelming majority of interesting Boolean functions and on the other hand it is small enough to prevent us from the necessity to take into account counting arguments. To illustrate the second point, let me remind the reader that already the class \Delta p 2 ,...
Approximating center points with iterated Radon points
 Internat. J. Comput. Geom. Appl
, 1996
"... We give a practical and provably good Monte Carlo algorithm for approximating center points. Let P be a set of n points in IR d. A point c ∈ IR d is a βcenter point of P if every closed halfspace containing c contains at least βn points of P. Every point set has a 1/(d + 1)center point; our algori ..."
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Cited by 55 (10 self)
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We give a practical and provably good Monte Carlo algorithm for approximating center points. Let P be a set of n points in IR d. A point c ∈ IR d is a βcenter point of P if every closed halfspace containing c contains at least βn points of P. Every point set has a 1/(d + 1)center point; our algorithm finds an Ω(1/d 2)center point with high probability. Our algorithm has a small constant factor and is the first approximate center point algorithm whose complexity is subexponential in d. Moreover, it can be optimally parallelized to require O(log 2 d log log n) time. Our algorithm has been used in mesh partitioning methods and can be used in the construction of high breakdown estimators for multivariate datasets in statistics. It has the potential to improve results in practice for constructing weak ɛnets. We derive a variant of our algorithm whose time bound is fully polynomial in d and linear in n, and show how to combine our approach with previous techniques to compute high quality center points more quickly. 1
Two applications of inductive counting for complementation problems
 SIAM Journal of Computing
, 1989
"... nondeterministic spacebounded complexity classes are closed under complementation, two further applications of the inductive counting technique are developed. First, an errorless probabilistic algorithm for the undirected graph st connectivity problem that runs in O(log n) space and polynomial exp ..."
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Cited by 53 (4 self)
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nondeterministic spacebounded complexity classes are closed under complementation, two further applications of the inductive counting technique are developed. First, an errorless probabilistic algorithm for the undirected graph st connectivity problem that runs in O(log n) space and polynomial expected time is given. Then it is shown that the class LOGCFL is closed under complementation. The latter is a special case of a general result that shows closure under complementation of classes defined by semiunbounded fanin circuits (or, equivalently, nondeterministic auxiliary pushdown automata or treesize bounded alternating Turing machines). As one consequence, it is shown that small numbers of "role switches " in twoperson pebbling can be eliminated.
On Monotone Formula Closure of SZK
, 1994
"... We investigate structural properties of statistical zero knowledge (SZK) both in the interactive and in the noninteractive model. Specifically, we look into the closure properties of SZK languages under monotone logical formula composition. This gives rise to new protocol techniques. We show that i ..."
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Cited by 41 (1 self)
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We investigate structural properties of statistical zero knowledge (SZK) both in the interactive and in the noninteractive model. Specifically, we look into the closure properties of SZK languages under monotone logical formula composition. This gives rise to new protocol techniques. We show that interactive SZK for random self reducible languages (RSR) (and for coRSR) is closed under monotone boolean operations. Namely, we give SZK proofs for monotone boolean formulae whose atoms are statements about an SZK language which is RSR (or a complement of RSR). All previously known languages in SZK are in these classes. We then show that if a language L has a noninteractive SZK proof system then honestverifier interactive SZK proof systems exist for all monotone boolean formulae whose atoms are statements about the complement of L. We also discuss extensions and generalizations. 1 Introduction Goldwasser, Micali, and Rackoff [34] introduced the notion of a zeroknowledge proof, a proof ...
Access control and signatures via quorum secret sharing
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 1998
"... We suggest a method of controlling the access to a secure database via quorum systems. A quorum system is a collection of sets (quorums) every two of which have a nonempty intersection. Quorum systems have been used for a number of applications in the area of distributed systems. We propose a separ ..."
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Cited by 34 (13 self)
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We suggest a method of controlling the access to a secure database via quorum systems. A quorum system is a collection of sets (quorums) every two of which have a nonempty intersection. Quorum systems have been used for a number of applications in the area of distributed systems. We propose a separation between access servers, which are protected and trustworthy, but may be outdated, and the data servers, which may all be compromised. The main paradigm is that only the servers in a complete quorum can collectively grant (or revoke) access permission. The method we suggest ensures that, after authorization is revoked, a cheating user Alice will not be able to access the data even if many access servers still consider her authorized and even if the complete raw database is available to her. The method has a low overhead in terms of communication and computation. It can also be converted into a distributed system for issuing secure signatures. An important building block in our method is the use of secret sharing schemes that realize the access structures of quorum systems. We provide several efficient constructions of such schemes which may be of interest in their own right.