Computer Science Technical Reports
Permanent URI for this collectionhttps://hdl.handle.net/2104/4824
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Browsing Computer Science Technical Reports by Subject "Design Automation"
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Item : GF2Matrices(2009-03-31T14:52:17Z) Maurer, Peter M.This is the software described in the technical report “The GF2Matrices Classes: A Programming Package for Mathematical Research.” Over the past few years I have been engaged in an intense study of GF(2) matrices, especially of dimensions 2, 3, 4, and 5. The software I used for this study was mostly a bunch of ad-hoc subroutines scattered over numerous projects. This package consolidates all of this software into a system of classes. This software can be used to reproduce any of my results. This package is distributed without any warranty of any kind.Item The GF2Matrices Classes: A Programming Package for Mathematical Research(2009-03-31T14:31:06Z) Maurer, Peter M.Over the past few years I have been engaged in an intense study of GF(2) matrices, especially of dimensions 2, 3, 4, and 5. The software I used for this study was mostly a bunch of ad-hoc subroutines scattered over numerous projects. This package consolidates all of this software into a system of classes. This software can be used to reproduce any of my results.Item Using GF(2) matrices in Simulation and Logic Synthesis(2009-01-23T16:31:18Z) Maurer, Peter M.GF(2) matrices are matrices of ones and zeros under modulo 2 arithmetic. Like the GF(2) polynomials used in error detection and correction, they have many potential uses in Electronic Design Automation (EDA). Non-singular matrices can be used to define new classes of symmetry called conjugate symmetries. Conjugate symmetries have been used to speed up certain kinds of functional-level simulations, and have other potential uses. GF(2) matrices can also be used to transform Boolean vector spaces and simplify Boolean functions. Although matrix transformations can be complex, simpler single-bit matrices can be used instead of general matrices. This simplifies the approach without loss of generality. Singular matrices can be used to reduce the complexity of certain functions, beyond what is normally possible with conventional simplification techniques. GF(2) matrices can also be used to define exotic symmetries called strange symmetries and collapsed symmetries. These exotic symmetries may prove useful in future EDA applications.Item Using GF2 Matrices to Simplify Boolean Logic(2009-01-23T19:40:41Z) Maurer, Peter M.Conventional logic simplification can be couched in terms of singular GF(2) matrices. The advantage to doing this is that different matrices can be used to combine terms that are separated by a Hamming distance greater than one. Although this sort of thing can be done without matrices, it is not clear what one would do after finding such terms. We show that by applying a matrix transformation to the inputs of a function, we can combine terms that are at arbitrary distances. We also show that we can further simplify functions by transforming the input vector space with a non-singular transformation.