[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science

24-26 Oct. 1988

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Displaying Results 1 - 25 of 60
  • Hardness vs. randomness

    Publication Year: 1988, Page(s):2 - 11
    Cited by:  Papers (29)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (577 KB)

    A simple construction for a pseudorandom bit generator is presented. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (e.g. P, NC, PSPACE, etc.), using an arbitrary function that is hard for C. This generator reveals an equivalence between the problems of proving lower bounds and the problem of generating good pseudora... View full abstract»

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  • On the existence of pseudorandom generators

    Publication Year: 1988, Page(s):12 - 24
    Cited by:  Papers (11)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (803 KB)

    Pseudorandom generators are known to exist, assuming the existence of functions that cannot be efficiently inverted on the distributions induced by applying the function iteratively polynomially many times. This sufficient condition is also necessary, but it is difficult to check whether particular functions, assumed to be one-way, are also one-way on their iterates. This raises the fundamental qu... View full abstract»

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  • Zero-knowledge with log-space verifiers

    Publication Year: 1988, Page(s):25 - 35
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (829 KB)

    Interactive proof systems are considered in which the best set of possible verifiers is restricted to the class of probabilistic log-space automata. A. Condon (1988) introduced this model and showed that if the protocols are allowed to run for arbitrarily many rounds, exponential-time languages can be proved to a log-space verifier. To better approximate the usual notion of interactive proof syste... View full abstract»

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  • Homogeneous measures and polynomial time invariants

    Publication Year: 1988, Page(s):36 - 41
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (273 KB)

    The usual probability distributions are concentrated on strings that do not differ noticeably in any fundamental characteristics, except their informational size (Kolmogorov complexity). The formalization of this statement is given and shown to distinguish a class of homogeneous probability measures suggesting various applications. In particular, it could explain why the average case NP-completene... View full abstract»

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  • Achieving oblivious transfer using weakened security assumptions

    Publication Year: 1988, Page(s):42 - 52
    Cited by:  Papers (55)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (809 KB)

    The authors present some general techniques for establishing the cryptographic strength of a wide variety of games. As case studies, they analyze some weakened versions of the standard forms of oblivious transfer. They also consider variants of oblivious transfer that are motivated by coding theory and physics. Among their results, they show that a noisy telephone line is in fact a very sophistica... View full abstract»

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  • Lower bounds for integer greatest common divisor computations

    Publication Year: 1988, Page(s):54 - 63
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (648 KB)

    An Omega (log log n) lower bound is proved on the depth of any computation tree with operations (+, -, /, mod, <or=) that computes the greatest common divisor (GCD) of all pairs of n-bit integers. A novel technique for handling the truncation operation is implicit in the proof. Also proved is a Theta (n) bound on the depth of any algebraic computation trees with operations (+, -, *, /, <or=)... View full abstract»

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  • A lower bound for matrix multiplication

    Publication Year: 1988, Page(s):64 - 67
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (182 KB)

    It is proved that computing the product of two n*n matrices over the binary field requires at least 2.5n/sup 2/-O(n/sup 2/) multiplications.<<ETX>> View full abstract»

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  • The influence of variables on Boolean functions

    Publication Year: 1988, Page(s):68 - 80
    Cited by:  Papers (106)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (729 KB)

    Methods from harmonic analysis are used to prove some general theorems on Boolean functions. These connections with harmonic analysis viewed by the authors are very promising; besides the results on Boolean functions they enable them to prove theorems on the rapid mixing of the random walk on the cube and in the extremal theory of finite sets.<<ETX>> View full abstract»

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  • Lattices, mobius functions and communications complexity

    Publication Year: 1988, Page(s):81 - 90
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (782 KB)

    A general framework for the study of a broad class of communication problems is developed. It is based on a recent analysis of the communication complexity of graph connectivity. The approach makes use of combinatorial lattice theory.<<ETX>> View full abstract»

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  • Near-optimal time-space tradeoff for element distinctness

    Publication Year: 1988, Page(s):91 - 97
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (401 KB)

    It was conjectured by A. Borodin et al. that to solve the element distinctness problem requires TS= Omega (n/sup 2/) on a comparison-based branching program using space S and time T, which, if true, would be close to optimal since TS=O(n/sup 2/ log n) is achievable. They showed recently (1987) that TS= Omega (n/sup 3/2/(log n)/sup 1/2/). The author shows a near-optimal tradeoff TS= Omega (n/sup 2-... View full abstract»

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  • 29th Annual Symposium on Foundations of Computer Science (IEEE Cat. No.88CH2652-6)

    Publication Year: 1988
    Request permission for commercial reuse | PDF file iconPDF (251 KB)
    Freely Available from IEEE
  • Predicting (0, 1)-functions on randomly drawn points

    Publication Year: 1988, Page(s):100 - 109
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (847 KB)

    The authors consider the problem of predicting (0, 1)-valued functions on R/sup n/ and smaller domains, based on their values on randomly drawn points. Their model is related to L.G. Valiant's learnability model (1984), but does not require the hypotheses used for prediction to be represented in any specified form. The authors first disregard computational complexity and show how to construct pred... View full abstract»

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  • Learning probabilistic prediction functions

    Publication Year: 1988, Page(s):110 - 119
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (974 KB)

    The question of how to learn rules, when those rules make probabilistic statements about the future, is considered. Issues are discussed that arise when attempting to determine what a good prediction function is, when those prediction functions make probabilistic assumptions. Learning has at least two purposes: to enable the learner to make predictions in the future and to satisfy intellectual cur... View full abstract»

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  • Results on learnability and the Vapnik-Chervonenkis dimension

    Publication Year: 1988, Page(s):120 - 129
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (724 KB)

    The problem of learning a concept from examples in a distribution-free model is considered. The notion of dynamic sampling, wherein the number of examples examined can increase with the complexity of the target concept, is introduced. This method is used to establish the learnability of various concept classes with an infinite Vapnik-Chervonenkis (VC) dimension. An important variation on the probl... View full abstract»

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  • Learning via queries

    Publication Year: 1988, Page(s):130 - 137
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (628 KB)

    The power of various query languages is compared along two dimensions, namely the inherent power of the language and the number of alternations of quantizers. Learning by asking questions is compared to learning by passively reading data. It is found that the extent of what can be learned by queries is largely dependent on the language used by the inference mechanism to formulate questions to ask ... View full abstract»

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  • Effect of connectivity in associative memory models

    Publication Year: 1988, Page(s):138 - 147
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (665 KB)

    The authors investigate how good connectivity properties translate into good error-correcting behavior in sparse networks of threshold elements. They determine how the eigenvalues of the interconnection graph (which in turn reflect connectivity properties) relate to the quantities, number of items stored, amount of error-correction, radius of attraction, and rate of convergence in an associative m... View full abstract»

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  • Efficient parallel algorithms for chordal graphs

    Publication Year: 1988, Page(s):150 - 161
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1005 KB)

    The author gives efficient parallel algorithms for recognizing chordal graphs, finding a maximum clique and a maximum independent set in a chordal graph, finding an optimal coloring of a chordal graph, finding a breadth-first search tree and a depth-first search tree of a chordal graph, recognizing interval graphs, and testing interval graphs for isomorphism. The key to the results is an efficient... View full abstract»

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  • Removing randomness in parallel computation without a processor penalty

    Publication Year: 1988, Page(s):162 - 173
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (703 KB)

    Some general techniques are developed for removing randomness from randomized NC algorithms without a blowup in the number of processors. One of the requirements for the application of these techniques is that the analysis of the randomized algorithm uses only pairwise independence. The main new result is a parallel algorithm for the Delta +1 vertex coloring problem with running time O(log/sup 3/ ... View full abstract»

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  • Sublinear-time parallel algorithms for matching and related problems

    Publication Year: 1988, Page(s):174 - 185
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (948 KB)

    The authors present the first sub-linear-time deterministic parallel algorithms for bipartite matching and several related problems, including maximal node-disjoint paths, depth-first search, and flows in zero-one networks. The results are based on a better understanding of the combinatorial structure of the above problems, which lead to new algorithmic techniques. In particular, it is shown how t... View full abstract»

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  • Optimal parallel algorithm for the Hamiltonian cycle problem on dense graphs

    Publication Year: 1988, Page(s):186 - 193
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (513 KB)

    G.A. Dirac's classical theorem (1952) asserts that if every vertex of a graph G on n vertices has degree at least n/2, the G has a Hamiltonian cycle. A fast parallel algorithm on a concurrent-read-exclusive-write parallel random-access machine (CREW PRAM) is given to find a Hamiltonian cycle in such graphs. The algorithm uses a linear number of processors and is optimal up to a polylogarithmic fac... View full abstract»

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  • Parallel comparison algorithms for approximation problems

    Publication Year: 1988, Page(s):194 - 203
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (742 KB)

    The authors consider that they have n elements from a totally ordered domain and are allowed to perform p parallel comparisons in each time unit (round). They determine, up to a constant factor, the time complexity of several approximation problems in the common parallel comparison tree model of L.G. Valiant, for all admissible values of n, p, and epsilon , where epsilon is an accuracy parameter d... View full abstract»

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  • Dynamic networks are as fast as static networks

    Publication Year: 1988, Page(s):206 - 219
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (910 KB)

    An efficient simulation is given to show that dynamic networks are as fast as static ones up to a constant multiplicative factor. That is, any task can be performed in a dynamic asynchronous network essentially as fast as in a static synchronous network. The simulation protocol is based on an approach in which locality is perceived as the key to fast adaptation to changes in network topology. The ... View full abstract»

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  • Increasing the size of a network by a constant factor can increase performance by more than a constant factor

    Publication Year: 1988, Page(s):221 - 230
    Cited by:  Papers (17)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (522 KB)

    In one routing scheme which has been implemented on a parallel architecture based on the butterfly graph, messages are sometimes destroyed. It is shown that if messages are sent to random destinations, the expected number of messages that reach their destinations is Theta (n(log n)-1/q), where n is the size of the butterfly graph and q is the number of messages that can move through one edge (or, ... View full abstract»

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  • On the effects of feedback in dynamic network protocols

    Publication Year: 1988, Page(s):231 - 245
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (936 KB)

    A framework is introduced that provides a unified way for proving correctness as well as analyzing performance of a class of communication protocols called (asynchronous) reset protocols. They are logarithmic transformers, converting protocols working in a static asynchronous network into protocols working in a dynamic asynchronous network. The design of reset protocols is a classical problem in c... View full abstract»

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  • Coordinated traversal: (t+1)-round Byzantine agreement in polynomial time

    Publication Year: 1988, Page(s):246 - 255
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (836 KB)

    The problem of efficiently performing Byzantine agreement in t+1 rounds in the face of arbitrarily malicious failures is treated. A communication-efficient polynomial-time protocol is presented for n>8t. The protocol is an early stopping protocol, halting in min(t+1, f+2) rounds in the worst case, where f is the number of processors that fail during the run. This is provably optimal. The protoc... View full abstract»

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