30th Annual Symposium on Foundations of Computer Science

Oct. 30 1989-Nov. 1 1989

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  • 30th Annual Symposium on Foundations of Computer Science (Cat. No.89CH2808-4)

    Publication Year: 1989
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    Freely Available from IEEE
  • Conductance and convergence of Markov chains-a combinatorial treatment of expanders

    Publication Year: 1989, Page(s):526 - 531
    Cited by:  Papers (23)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (400 KB)

    A direct combinatorial argument is given to bound the convergence rate of Markov chains in terms of their conductance (these are statements of the nature `random walks on expanders converge fast'). In addition to showing that the linear algebra in previous arguments for such results on time-reversible Markov chains was unnecessary, the direct analysis applies to general irreversible Markov chains View full abstract»

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  • An analogue of the Myhill-Nerode theorem and its use in computing finite-basis characterizations

    Publication Year: 1989, Page(s):520 - 525
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (448 KB)

    A theorem that is a graph-theoretic analog of the Myhill-Nerode characterization of regular languages is proved. The theorem is used to establish that for many applications obstruction sets are computable by known algorithms. The focus is exclusively on what is computable (by a known algorithm) in principle, as opposed to what is computable in practice View full abstract»

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  • On the computational power of PP and ⊕P

    Publication Year: 1989, Page(s):514 - 519
    Cited by:  Papers (48)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (344 KB)

    Two complexity classes, PP and ⊕P, are compared with PH (the polynomial-time hierarchy). The main results are as follows: (1) every set in PH is reducible in a certain sense to a set in PP, an (2) every set in PH is reducible to a set in ⊕P under randomized polynomial-time reducibility with two-sided bounded error probability. It follows from these results that neither PP nor ⊕P ... View full abstract»

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  • On the network complexity of selection

    Publication Year: 1989, Page(s):396 - 401
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (544 KB)

    The sequential complexity of determining the kth largest out of a given set of n keys is known to be linear. Thus, given a p-processor parallel machine, it is asked whether or not an O(n/p) selection algorithm can be devised for that machine. An Ω((n/p) log log p+log p) lower bound is obtained for selec... View full abstract»

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  • Area-optimal three-layer channel routing

    Publication Year: 1989, Page(s):506 - 511
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (400 KB)

    The channel routing problem in the knock-knee mode is considered. The algorithm presented always constructs a correct layout in a channel of bounded size, if there is one, and guarantees that it is wirable with only three conducting layers; that is, the layout is optimal with respect to the area and to the number of layers. The algorithm thus improves all previously known layout algorithms, which ... View full abstract»

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  • A randomized maximum-flow algorithm

    Publication Year: 1989, Page(s):118 - 123
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (488 KB)

    The authors present a randomized maximum-flow algorithm, called the PLED (prudent linking excess diminishing) algorithm, whose expected running time is O(nm+n2(log n )3); this is O(nm) for all except relatively sparse networks. The algorithm is always correct, and in the worst case, which occurs with negligible probability... View full abstract»

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  • Efficient simulations of small shared memories on bounded degree networks

    Publication Year: 1989, Page(s):390 - 395
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (452 KB)

    The problem of simulating a parallel random-access machine (PRAM) with n processors and memory size m⩾n on an n-node bounded degree network (BDN) is considered. Since many of the more efficient PRAM algorithms use an amount of shared memory not much larger than the number of processors, the case in which m=o(n1+ε) i... View full abstract»

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  • Double precision geometry: a general technique for calculating line and segment intersections using rounded arithmetic

    Publication Year: 1989, Page(s):500 - 505
    Cited by:  Papers (4)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (532 KB)

    For the first time it is shown how to reduce the cost of performing specific geometric constructions by using rounded arithmetic instead of exact arithmetic. By exploiting a property of floating-point arithmetic called monotonicity, a technique called double-precision geometry can replace exact arithmetic with rounded arithmetic in any efficient algorithm for computing the set of intersections of ... View full abstract»

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  • Flow in planar graphs with multiple sources and sinks

    Publication Year: 1989, Page(s):112 - 117
    Cited by:  Papers (5)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (504 KB)

    Given a planar network with many sources and sinks, the problem of computing the maximum flow from the sources to the sinks is investigated. An algorithm that runs in O(log2n ) time using O(n1.5) processors on an exclusive-read-exclusive-write parallel random-access machine (EREW PRAM) is obtained, when the amount of flow (demand) at each s... View full abstract»

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  • Expanders might be practical: fast algorithms for routing around faults on multibutterflies

    Publication Year: 1989, Page(s):384 - 389
    Cited by:  Papers (37)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (592 KB)

    Simple deterministic O(log N)-step algorithms for routing packets on a multibutterfly are described. The algorithms are shown to be robust against faults, even in the worst case, and to be efficient from a practical point of view. As a consequence, the multibutterfly is shown to be an excellent candidate for a high-bandwidth, low-diameter switching network underlying a distribute... View full abstract»

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  • Stable maintenance of point set triangulations in two dimensions

    Publication Year: 1989, Page(s):494 - 499
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (596 KB)

    Geometric algorithms are explored, assuming that arithmetic is done approximately. Stable algorithms are described for two geometric problems. The first algorithm computes two-dimensional convex hulls. The main result is that a triangulation of a set of points in the plane can be maintained stably. The second algorithm deals with line arrangements in the plane View full abstract»

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  • Efficient algorithms for independent assignment on graphic and linear matroids

    Publication Year: 1989, Page(s):106 - 111
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (540 KB)

    Efficient algorithms are presented for the matroid intersection problem and generalizations. The algorithm for weighted intersection works by scaling the weights. The cardinality algorithm is a special case that takes advantage of greater structure. Efficiency of the algorithms is illustrated by several implementations. On graphic matroids the algorithms run close to the best bounds for trivial ma... View full abstract»

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  • The synchronization of nonuniform networks of finite automata

    Publication Year: 1989, Page(s):376 - 381
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (548 KB)

    The generalized firing squad synchronization problem (GFSSP) is the well-known firing squad synchronization problem extended to arbitrarily connected networks of finite automata. When the transmission delays associated with the links of a network are allowed to be arbitrary nonnegative integers, the problem is called GFSSP-NUD (GFSSP with nonuniform delays). A solution of GFSSP-NUD is given for th... View full abstract»

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  • Dynamically computing the maxima of decomposable functions, with applications

    Publication Year: 1989, Page(s):488 - 493
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (496 KB)

    The authors present a general technique for updating the maximum (minimum) value of a decomposable function as elements are inserted into and deleted from the set S. Applications of this technique include efficient algorithms for dynamically computing the diameter or closest pair of a set of points, minimum separation among a set of rectangles, smallest distance between a set of points an... View full abstract»

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  • The equivalence and learning of probabilistic automata

    Publication Year: 1989, Page(s):268 - 273
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (412 KB)

    It is proved that the equivalence problem for probabilistic automata is solvable in time O((n1+n 2)4), where n1 and n 2 are numbers of states of two given probabilistic automata. This result improves the best previous upper bound of coNP. The algorithm has some interesting applications, for example,... View full abstract»

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  • Solvability in asynchronous environments

    Publication Year: 1989, Page(s):422 - 427
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (440 KB)

    The authors present necessary and sufficient combinatorial conditions that determine membership in SMt (respectively, MPt), the class of distributed decision tasks that are solvable in the shared memory (resp. message passing) model by a t-resilient randomized protocol, which never errs and works in the presence of a strong adversary. The sufficienc... View full abstract»

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  • Galois groups and factoring polynomials over finite fields

    Publication Year: 1989, Page(s):99 - 104
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (468 KB)

    Let p be a prime and F be a polynomial with integer coefficients. Suppose that the discriminant of F is not divisible by p, and denote by m the degree of the splitting field of F over Q and by L the maximal size of the coefficients of F. Then, assuming the generalized Riemann hypothesis (GRH), it is shown that the irr... View full abstract»

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  • A really temporal logic

    Publication Year: 1989, Page(s):164 - 169
    Cited by:  Papers (48)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (484 KB)

    A real-time temporal logic for the specification of reactive systems is introduced. The novel feature of the logic, TPTL, is the adoption of temporal operators as quantifiers over time variables; every modality binds a variable to the time(s) it refers to. TPTL is demonstrated to be both a natural specification language and a suitable formalism for verification and synthesis. A tableau-based decis... View full abstract»

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  • Upper and lower bounds for routing schemes in dynamic networks

    Publication Year: 1989, Page(s):370 - 375
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (504 KB)

    An algorithm and two lower bounds are presented for the problem of constructing and maintaining routing schemes in dynamic networks. The algorithm distributively assigns addresses to nodes and constructs routing tables in a dynamically growing tree. The resulting scheme routes data messages over the shortest path between any source and destination, assigns addresses of O(log2 View full abstract»

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  • A note on the power of threshold circuits

    Publication Year: 1989, Page(s):580 - 584
    Cited by:  Papers (37)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (292 KB)

    The author presents a very simple proof of the fact that any language accepted by polynomial-size depth-k unbounded-fan-in circuits of AND and OR gates is accepted by depth-three threshold circuits of size n raised to the power O(logk n). The proof uses much of the intuition of S. Toda's result that the polynomial hierarchy is contained in P#P View full abstract»

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  • An upper bound on the number of planar k-sets

    Publication Year: 1989, Page(s):72 - 79
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (452 KB)

    Given a set S of n points, a subset X of size k is called a k-set if there is a hyperplane II that separates X from Xc. It is proved that O(n√k/log*k) is an upper bound for the number of k-sets in the plane, thus improving the previous bound of P. Erdos et al. (A ... View full abstract»

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  • Speeding-up linear programming using fast matrix multiplication

    Publication Year: 1989, Page(s):332 - 337
    Cited by:  Papers (26)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (420 KB)

    The author presents an algorithm for solving linear programming problems that requires O((m+n)1.5 nL) arithmetic operations in the worst case, where m is the number of constraints, n the number of variables, and L a parameter defined in the paper. This result improves on the best known time complexity for linear programming ... View full abstract»

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  • On the power of 2-way probabilistic finite state automata

    Publication Year: 1989, Page(s):480 - 485
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (436 KB)

    The recognition power of two-way probabilistic finite-state automata (2PFAs) is studied. It is shown that any 2PFA recognizing a nonregular language must use exponential expected time infinitely often. The power of interactive proof systems (IPSs) where the verifier is a 2PFA is also investigated. It is shown that (1) IPSs in which the verifier uses private randomization are strictly more powerful... View full abstract»

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  • On the complexity of learning from counterexamples

    Publication Year: 1989, Page(s):262 - 267
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (472 KB)

    The complexity of learning concepts belonging to various concrete concept classes C⊆2X over a finite domain X is analyzed in terms of the number of counterexamples that are needed in the worst case. It turns out that for many interesting concept classes there exist exponential differences between the number of counterexamples that are required by a `naive' learni... View full abstract»

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