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Algorithmic Aspects of Symbolic Switch Network Analysis
 IEEE Trans. CAD/IC
, 1987
"... A network of switches controlled by Boolean variables can be represented as a system of Boolean equations. The solution of this system gives a symbolic description of the conducting paths in the network. Gaussian elimination provides an efficient technique for solving sparse systems of Boolean eq ..."
Abstract

Cited by 16 (5 self)
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A network of switches controlled by Boolean variables can be represented as a system of Boolean equations. The solution of this system gives a symbolic description of the conducting paths in the network. Gaussian elimination provides an efficient technique for solving sparse systems of Boolean equations. For the class of networks that arise when analyzing digital metaloxide semiconductor (MOS) circuits, a simple pivot selection rule guarantees that most s switch networks encountered in practice can be solved with O(s) operations. When represented by a directed acyclic graph, the set of Boolean formulas generated by the analysis has total size bounded by the number of operations required by the Gaussian elimination. This paper presents the mathematical basis for systems of Boolean equations, their solution by Gaussian elimination, and data structures and algorithms for representing and manipulating Boolean formulas.
Parallel Output Sensitive Algorithms for Combinatorial and Linear Algebra Problems
, 2000
"... This paper gives output sensitive parallel algorithms whose performance ..."
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Cited by 2 (2 self)
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This paper gives output sensitive parallel algorithms whose performance
Generalized Scans and TriDiagonal Systems
"... Motivated by the analysis of known parallel techniques for the solution of linear tridiagonal system, weintroduce generalized scans, a class of recursively de#ned lengthpreserving, sequencetosequence transformations that generalize the wellknown pre#x computations #scans#. Generalized scan functi ..."
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Motivated by the analysis of known parallel techniques for the solution of linear tridiagonal system, weintroduce generalized scans, a class of recursively de#ned lengthpreserving, sequencetosequence transformations that generalize the wellknown pre#x computations #scans#. Generalized scan functions are described in terms of three algorithmic phases, the reduction phase that saves data for the third or expansion phase and prepares data for the second phase which is a recursiveinvocation of the same function on one fewer variable. Both the reduction and expansion phases operate on bounded numberofvariables, a key feature for their parallelization. Generalized scans enjoya property, called here protoassociativity, that gives rise to ordinary associativity when generalized scans are specialized to ordinary scans. We show that the solution of positive de#nite block tridiagonal linear systems can be cast as a generalized scan, thereby shedding light on the underlying structure enabling k...
On the Power of Discontinuous Approximate Computations
, 1991
"... Comparision operations are used in algebraic computations to avoid degeneracies, but are also used in numerical computations to avoid huge roundoff errors. On the other hand ..."
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Comparision operations are used in algebraic computations to avoid degeneracies, but are also used in numerical computations to avoid huge roundoff errors. On the other hand
2.2 Some Computations Related to Matrix Multiplication.............. 6 2.3 Gaussian Elimination Algorithm.......................... 7
"... 2 Supported by the European Union under ESPRIT FRISCO project LTR 21.024. 3 ..."
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2 Supported by the European Union under ESPRIT FRISCO project LTR 21.024. 3
APPLICATIONS OF FFT 1
"... The subject of this chapter lies in the area of theoretical computer science, though it borrows certain results from computational mathematics, and is fundamental to the theory and practice of signal and image processing and scienti c and engineering computing. A central theme is to bridge the gap b ..."
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The subject of this chapter lies in the area of theoretical computer science, though it borrows certain results from computational mathematics, and is fundamental to the theory and practice of signal and image processing and scienti c and engineering computing. A central theme is to bridge the gap between polynomial arithmetic on the one hand, and
APPLICATIONS OF FFT 1
"... The subject of this chapter lies in the area of theoretical computer science, though it borrows certain results from computational mathematics, and is fundamental to the theory and practice of signal and image processing and scienti c and engineering computing. A central theme is to bridge the gap b ..."
Abstract
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The subject of this chapter lies in the area of theoretical computer science, though it borrows certain results from computational mathematics, and is fundamental to the theory and practice of signal and image processing and scienti c and engineering computing. A central theme is to bridge the gap between polynomial arithmetic on the one hand, and