# Computer Science Technical Reports

Permanent URI for this collectionhttps://hdl.handle.net/2104/4824

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Item Anti-Symmetry and Logic Simulation(2012-01-19) Maurer, Peter M.Like ordinary symmetries, anti-symmetries are defined in terms of relations between function cofactors. For ordinary symmetries, two cofactors must be equal, for anti-symmetries two cofactors must be complements of another. It is known that ordinary symmetries can be used to improve simulation performance, but up until this point, it has not been known whether anti-symmetries could be used for this purpose. This paper shows that anti-symmetries can be as effective in boosting simulation performance as ordinary symmetries, sometimes even more so. Detailed detection and simulation algorithms are given along with a set of experimental results to show the effectiveness of the algorithms.Item AN APPLICATION OF GROUP THEORY TO THE ANALYSIS OF SYMMETRIC GATES(2009-10-26T15:35:05Z) Maurer, Peter M.A method for determining the symmetries of the inputs of a logic gate either from its truth table or from facts obtained by inspection of its circuit is presented. The symmetry rule of a gate with n inputs is defined in terms of a subgroup of the symmetric group of degree n. This technique leads to an expanded and more complete definition of partial symmetry than has previously appeared. This definition of symmetry is used to show that the set of Boolean expressions that represent non-totally-symmetric functions is NP-complete. The group-theoretic concept of conjugate sets is used to identify symmetry rules that are fundamentally the same but applied to different sets of inputs. A complete analysis of all forms of symmetry for 2-input, 3-input and 4-input gates is provided. An example is given to show how this theory was applied to a problem in VLSI design verification.Item Bootstrapping Bipartite Graphs Consisting of Edges Based on Ontology Terms Occurring in Scientific Abstract(2011-05-13T15:33:14Z) Morillo, DanielThe Ontological Discovery Environment (ODE) provides an efficient structure for storage of gene and pheno- type relations. The relations can be represented by a bipartite graph, where the gene and phenotype items can be described as independent sets. By creating a phenome interdependency and similarity hierarchy (PhISH), the bipartite graph can be used to generate a hierarchy shaped by the similarities found in the properties of the graph nodes. The first objective for this project involves extending the PhISH diagram concept by applying its approach to other discrete data sets that can be represented with a bipartite graph, such as ontological terms and published articles that reference these terms. We apply this procedure to a subset of PubMed abstracts and mammalian phenotype ontological terms. The second objective for this project is to develop or implement a tool that would reveal significant hierarchies in the data, since the true scope of interaction is unknown. Bootstrapping is intended to reveal portions of the hierarchy that have stronger similarities to each other. In combination with the PhISH diagram, the bootstrapped data can show what ontology terms have strong similarities based on how they are encountered together in scientific abstracts.Item Categories for Component Level Design(2009-02-18T17:21:56Z) Maurer, Peter M.Several research problems are discussed, including communication mechanisms and the interface between components and the glue logic used to tie them together. A technique for engineering new component-level applications is presented. This technique divides an application into a set of tightly coupled parts each one of which can be placed in a specific category. Each of these categories has its own design methodology, most of which rely heavily on object oriented design. Once the features of an application have been divided into categories, they can be implemented as off- the-shelf components, new components, or as glue logic. The categorization scheme gives guidelines for the placement of each feature. The categorization scheme relies on the ability to pass pointers complex objects between components. The dangers of such practices are discussed, and suggestions are made for future research that might help mitigate these dangers.Item The Class 1 4x4 Faithful Representations of S4 over GF(2)(2013-09-20) Maurer, Peter M.There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 1.Item The Class 10 4x4 Faithful Representations of S4 over GF(2)(2013-09-20) Maurer, Peter M.There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 10. (There is no class 6, so the classes are numbered 1, 2, 3, 4, 5, 7, 8, 9, and 10.)Item The Class 2 4x4 Faithful Representations of S4 over GF(2)(2013-09-20) Maurer, Peter M.There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 2.Item The Class 3 4x4 Faithful Representations of S4 over GF(2)(2013-09-20) Maurer, Peter M.There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 3.Item The Class 4 4x4 Faithful Representations of S4 over GF(2)(2013-09-20) Maurer, Peter M.There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 4.Item The Class 5 4x4 Faithful Representations of S4 over GF(2)(2013-09-20) Maurer, Peter M.There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 5.Item The Class 7 4x4 Faithful Representations of S4 over GF(2)(2013-09-20) Maurer, Peter M.There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 7.Item The Class 8 4x4 Faithful Representations of S4 over GF(2)(2013-09-20) Maurer, Peter M.There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 8. This class includes the standard representation in permutation matrices.Item Class 9 4x4 Faithful Representations of S4 over GF(2)(2013-09-20) Maurer, Peter M.There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 9.Item The Complexity of Detecting Symmetric Functions(2009-02-18T17:23:29Z) Maurer, Peter M.The characterization of the symmetries of boolean functions is important both in automatic layout synthesis, and in automatic verification of manually created layouts. It is possible to characterize the symmetries of an n-input boolean function as an arbitrary subgroup, G, of S(n), the symmetric group of order n. Given an expression e, which represents an n-input boolean function F, and a subgroup G of S(n) the problem of whether F possesses symmetry G is an NP-complete problem. The concept of an orbit can be used to characterize the various types of symmetry for a specified number of inputs. This classification can then be used, along with a few partitioning rules to completely determine the symmetries of a Boolean function. This technique requires that the truth-table of a function be completely enumerated, and thus has a running time proportional to 2^n where n is the number of inputs of the function. Some of the mathematical concepts presented to support the NP-completeness result have intriguing possibilities for circuit minimization.Item The Conjugacy Classes of 3x3 and 4x4 Matrices Over GF(2)(2013-09-20) Maurer, Peter M.The general linear groups over GF(2) have an intricate and interesting structure. This report does some preliminary work in examining the structure of two of these groups by giving the conjugacy classes of 3x3 and 4x4 matrices over GF(2).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 Connlib(2009-11-13T15:33:47Z) Maurer, Peter M.This software package can be used to create the FHDL library file. This library allows one to use the FHDL parser and simulator software in your own projects. The package can be compiled either under Linux (i.e. gcc) or under Visual C++. A Makefile is provided for Linux compilation, and Visual C++ project files (Version 8) are provided for compilation under Visual C++. Compilation under Visual C++ requires special compilation steps to be inserted for the .yacc, .lex and .data (mkwhat) files. This software package requires prior installation of the Mkwhat package, also available on this site. In addition, the open source packages yacc (byacc), flex, and gcc must be installed. The gcc package may be omitted if you don’t use the output generation routines of the connlib package. However, the output of these routines is targeted for gcc. (It may work under other compilers but has not been so tested.) The library has two different names depending on whether it has been compiled under Linux or Visual C++. The Visual C++ name is “connlib.lib” while the Linux name is “libconn.a”.Item Deduction by Induction(2009-10-26T15:36:19Z) Maurer, Peter M.In this report, I offer a technique for computing power sums that is: intuitive, well-motivated, generalizable to all k, and suitable for presentation to pre-calculus students.Item Designing a Capstone Course to Simulate the Industrial Environment(2009-10-26T15:40:33Z) Speegle, Gregory David.The creation of a capstone course for an un- dergraduate computer science curriculum mirrors traditional software design. Initially, a high-level goal is created. This is refined into lower-level specifications by conducting interviews with the users. The implementation is based on these specifications. In our case, the capstone course is to simulate (as much as possible) the student experiences after graduation. Lower level specifications are created by approximately 20 hours of interviews with developers, testers and project managers in consulting, development and information technology departments. The results of these interviews are synthesized into a capItem Efficient M-fold Cross-validation Algorithm for KNearest Neighbors(2010-08-12T20:37:24Z) Meng, LeiThis project investigates m-fold cross-validation algorithms for automatic selection of k with k-nearest neighbors problems. An algorithm taxonomy is used to identify different m-fold cross-validation algorithms. The taxonomy contains three elements: the order of computing, the number of indexes and the number of threads. Different combinations of these elements produce different algorithms. Ten reasonable algorithms are implemented and tested on four datasets. These datasets are of different dimensions and different sizes. By analyzing the performance and results of these ten algorithms, the functionality of different elements in the taxonomy in different situation is identified.