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 metal-oxide 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.

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This paper gives output sensitive parallel algorithms whose performance

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, sequence-to-sequence transformations that generalize the well-known 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...

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