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Nicholas Pippenger

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

20 papers
2 author rows

Possible papers

20

FOCS Conference 1997 Conference Paper

The Computational Complexity of Knot and Link Problems

  • Joel Hass
  • J. C. Lagarias 0001
  • Nicholas Pippenger

We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted (that is, whether it is capable of being continuously deformed without self-intersection so that it lies in a plane). We show that this problem, UNKNOTTING PROBLEM, is in NP. We also consider the problem, SPLITTING PROBLEM, of determining whether two or more such polygons can be split (that is, whether they are capable of being continuously deformed without self-intersection so that they occupy both sides of a plane without intersecting it), and show that it also is in NP. Finally, we show that the problem of determining the genus of a polygonal knot (a generalization of the problem of determining whether it is unknotted) is in PSPACE.

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FOCS Conference 1990 Conference Paper

Faster Circuits and Shorter Formulae for Multiple Addition, Multiplication and Symmetric Boolean Functions

  • Mike Paterson
  • Nicholas Pippenger
  • Uri Zwick

A general theory is developed for constructing the shallowest possible circuits and the shortest possible formulas for the carry-save addition of n numbers using any given basic addition unit. More precisely, it is shown that if BA is a basic addition unit with occurrence matrix N, then the shortest multiple carry-save addition formulas that could be obtained by composing BA units are of size n/sup 1/p+o(1)/, where p is the unique real number for which the L/sub p/ norm of the matrix N equals 1. An analogous result connects the delay matrix M of the basic addition unit BA and the minimal q such that multiple carry-save addition circuits of depth (q+o(1)) log n could be constructed by combining BA units. On the basis of these optimal constructions of multiple carry-save adders, the shallowest known multiplication circuits are constructed. >

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FOCS Conference 1985 Conference Paper

On Networks of Noisy Gates

  • Nicholas Pippenger

We show that many Boolean functions (including, in a certain sense, "almost all" Boolean functions) have the property that the number of noisy gates needed to compute them differs from the number of noiseless gates by at most a constant factor. This may be contrasted with results of von Neumann, Dobrushin and Ortyukov to the effect that (1) for every Boolean function, the number of noisy gates needed is larger by at most a logarithmic factor, and (2) for some Boolean functions, it is larger by at least a logarithmic factor.

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FOCS Conference 1984 Conference Paper

Parallel Communication with Limited Buffers (Preliminary Version)

  • Nicholas Pippenger

Currently known parallel communication schemes allow n nodes interconnected by arcs (in such a way that each node meets only a fixed number of arcs) to transmit n packets according to an arbitrary permutation in such a way that (1) only one packet is sent over a given arc at any step, (2) at most 0(log n) packets reside at a given node at any time and (3) with high probability, each packet arrives at its destination within 0(log n) steps. We present and analyze a new parallel communication scheme that ensures that at most a fixed number of packets reside at a given node at any time.

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FOCS Conference 1979 Conference Paper

On Simultaneous Resource Bounds (Preliminary Version)

  • Nicholas Pippenger

It is well known that time bounds for machines correspond closely to size bounds for networks, and that space bounds correspond to depth bounds. It is not known whether simultaneous time and space bounds correspond to simultaneous size and depth bounds. It is shown here that simultaneous time and "reversal" bounds correspond to simultaneous size and depth bounds, and that simultaneous time and space bounds correspond to simultaneous size and "width" bounds.

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