Theory and Algorithms Commons^™

On Monotone Formulae With Restricted Depth, Maria M. Klawe, Wolfgang J. Paul, Nicholas J. Pippenger, Mihalis Yannakakis

All HMC Faculty Publications and Research

We prove a hierarchy theorem for the representation of monotone Boolean functions by monotone Boolean functions by monotone formulae with restricted depth. Specifically, we show that there are functions with Π_k-formulae of size n for which every Σ_k-formula has size exp Ω(n^1/(k-1)). A similar lower bound applies to concrete functions such as transitive closure and clique. We also show that any function with a formula of size n (and any depth) has a Σ_k-formula of size exp O(n^1/(k-1)). Thus our hierarchy theorem is the best possible.

Probabilistic Simulations, Nicholas J. Pippenger

All HMC Faculty Publications and Research

The results of this paper concern the question of how fast machines with one type of storage media can simulate machines with a different type of storage media. Most work on this question has focused on the question of how fast one deterministic machine can simulate another. In this paper we shall look at the question of how fast a probabilistic machine can simulate another. This approach should be of interest in its own right, in view of the great attention that probabilistic algorithms have recently attracted.

A Direct Formulation And Computer-Implementation Of A Symbolic Network Analysis Algorithm, Timothy James Knerr

Electrical & Computer Engineering Theses & Dissertations

An algorithm for the symbolic analysis of linear, time-invariant, active or passive networks is presented. The algorithm incorporates the best features of earlier numerical and topological methods of symbolic analysis. A hybrid set of equations is formulated for a closed linear graph and arranged in matrix form. A numerical evalu­ation procedure for the determinant of this hybrid matrix results in an efficient method of symbolic analysis. A proof of the algorithm based on determinant evaluation by a permutation product expansion provides insight into relationships with other methods of symbolic analysis. A computer program implementation of the algorithm is described and …

Algorithms For Pipe Network Analysis And Their Reliability, Don J. Wood

KWRRI Research Reports

Algorithms for analyzing steady state flow conditions in pipe networks are developed for general applications. The algorithms are based on both loop equations expressed in terms of unknown flowrates and node equations expressed in terms of unknown grades. Five methods, which represent those in significant use today, are presented. An example pipe network is analyzed to illustrate the application of the various algorithms. The various assumptions required for the different methods are presented and the methods are compared within a common framework.

The reliabilities of these commonly employed algorithms for pipe network analysis are investigated by analyzing a large number …

A Dimensionality Reduction Algorithm For The Karhunen Loeve Transform, Salomi T. Charalambous

Computational Modeling & Simulation Engineering Theses & Dissertations

The Karhunen Loeve Transform has conclusively been shown to be the optimum data compression algorithm for signals belonging to the same second order stationary process. Consequently, researchers have been searching for a fast implementation for the transform. Fast imple­mentation methods similar to those developed for other orthogonal transforms are generally not applicable to the Karhunen Loeve Transform (KLT). Also, since the basis vectors composing the transformation matrix of the KLT are the eigenvectors of the covariance matrix of the input process, they must be computed first. The research re­ ported here is an attempt to reduce the dimensionality of the …

Comparative Schematology And Pebbling With Auxiliary Pushdowns, Nicholas J. Pippenger

All HMC Faculty Publications and Research

This paper has three claims to interest. First, it combines comparative schematology with complexity theory. This combination is capable of distinguishing among Strong's “languages of maximal power,” a distinction not possible when comparative schematology is based on computability considerations alone, and it is capable of establishing exponential disparities in running times, a capability not currently possessed by complexity theory alone. Secondly, this paper inaugurates the study of pebbling with auxiliary pushdowns, which bears to plain pebbling the same relationship as Cook's study of space-bounded machines with auxiliary pushdowns bears to plain space-bounded machines. This extension of pebbling serves as the …

An Algorithm For The Electromagnetic Scattering Due To An Axially Symmetric Body With An Impedance Boundary Condition, F. Stenger, M. Hagmann, J. Scheing

Computer Science Faculty Publications

Let B be a body in R³, and let S denote the boundary of B. The surface S is described by S = {(x, y, z): (x² + Y²)^½= ƒ(z), -1≤ z ≤ I}, where ƒ analytic function that is real and positive on (-1, 1) and ƒ(±1) = 0. An algorithm is described for computing the scattered field due to a plane wave incident field, under Leontovich boundary conditions. The Galerkin method of solution used here leads to a block diagonal matrix involving 2M …

Determiningeons : A Computer Program For Approximating Lie Generators Admitted By Dynamical Systems, Gregory G. Nagao

University of the Pacific Theses and Dissertations

As was recognized by same of the most reputable physicists of the world such as Galilee and Einstein, the basic laws of physics must inevitably be founded upon invariance principles. Galilean and special relativity stand as historical landmarks that emphasize this message. It's no wonder that the great developments of modern physics (such as those in elementary particle physics) have been keyed upon this concept.

The modern formulation of classical mechanics (see Abraham and Marsden [1]) is based upon "qualitative" or geometric analysis. This is primarily due to the works of Poincare. Poincare showed the value of such geometric analysis …

An Efficient Dft Algorithm Using The Walsh Transform, Albert P. Gerheim

Electrical & Computer Engineering Theses & Dissertations

The matrix transformation relating the sequency and frequency domains is derived. It is shown that these­ frequency-to-frequency conversion can be performed via a computationally efficient sparse matrix algorithm. The sequency-to-frequency algorithm can be used with a fast Hadamard transform to implement a discrete Fourier trans­ form. The efficiencies of this combined algorithm and a radix-two fast Fourier transform are compared.

The algorithm is applied to the sequency domain de­ sign of a Wiener digital filter. Improved computational efficiencies are achieved relative to the procedure de­veloped by Kahveci and Hall (9).

An Algorithm For Finding All Isomorphisms Of Two Graphs, Atanas Radenski

Mathematics, Physics, and Computer Science Faculty Articles and Research

No abstract provided.