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 "Conjugate Symmetry"
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Item Conjugates of the Standard Representation of S3 in 3x3 matrices(2013-09-20) Maurer, Peter M.This is a list of the 28 conjugates of the standard representation of S3 in 3x3 matrices.Item Extending Symmetric Variable-Pair Transitivities Using State-Space Transformations(2011-05-13T15:29:52Z) Maurer, Peter M.Two-cofactor relations and their associated symmetry types have been studied for many years. While ordinary symmetries are simply transitive permitting them to be combined into clusters of variables, other types of symmetries have more complex transitivities. This paper shows how to convert the various types of symmetry into ordinary symmetries using state-space transformations. This permits the simple transitivity of ordinary symmetry to be extended to virtually any type of symmetry.Item The Hyper-Linear Package(2009-11-13T15:51:23Z) Maurer, Peter M.The Hyper-Linear package is the core of the hyper-linear simulation technique described in Reference 1. Given the specification of a Boolean function, the package will detect all partial and total symmetries and return the appropriate multi-dimensional hyper-linear structure. This structure can then be probed for the purpose of generating simulation code. This version of the Hyper-Linear package has the tweaks necessary for detecting conjugate symmetry. Use of conjugate symmetry is the default, but this can be suppressed by using lower-level function calls.Item HyperSim(2009-11-13T15:46:08Z) Maurer, Peter M.This software package implements the simulation algorithm described in the tech report “Using GF(2) matrices in Simulation and Logic Synthesis” found in this archive. (http://hdl.handle.net/2104/5263). This package is part of the FHDL system. Two executable files are produced HyperSim(.exe) and HyperSimA(.exe). HyperSimA is the preferred implementation. This package depends on the connlib and hyper2 packages also available from this archive.Item The Number of Conjugates of the Standard Representation of Sn in the General Linear Group over GF(2)(2013-09-20) Maurer, Peter M.This report determines the normalizer of the standard representation of Sn in the general linear group of nxn matrices over GF(2). The size of the normalizer is then used to determine the number of classes of conjugate symmetry for the general case.Item Why is Symmetry So Hard?(2011-05-13T15:28:18Z) Maurer, Peter M.The problem of detecting virtually any type of symmetry is shown to be co-NP-complete. We start with totally symmetric functions, then extend the result to partially symmetric functions, then to more general cofactor relations, and finally to generic permutation-group symmetries. We also show that the number of types of symmetry grows substantially with the number of inputs, compounding the complexity of an already difficult problem.