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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.
An Algebra of Switching Networks
, 2012
"... Is it right, that regardless of the existence of the already elaborated algebra of logic, the specific algebra of switching networks should be considered as a utopia? Paul Ehrenfest, 1910 A switch, whether mechanical or electrical, is a fundamental building element of digital systems. The theory of ..."
Abstract
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Is it right, that regardless of the existence of the already elaborated algebra of logic, the specific algebra of switching networks should be considered as a utopia? Paul Ehrenfest, 1910 A switch, whether mechanical or electrical, is a fundamental building element of digital systems. The theory of switching networks, or simply circuits, dates back to Shannon’s thesis (1937), where he employed Boolean algebra for reasoning about the functionality of switching networks, and graph theory for describing and manipulating their structure. Following this classic approach, one can deduce functionality from a given structure via analysis, and create a structure implementing a specified functionality via synthesis. The use of two different mathematical languages creates a ‘language barrier ’ – whenever a circuit description is changed in one language, it is necessary to translate the change into the other one to keep both descriptions in sync. For example, having tweaked a circuit structure one cannot be certain that the circuit functionality has not been broken, and vice versa.