Technical Reports

Metamorphosis, State Machines, and Object Oriented Design

2007-05-31T18:36:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

Metamorphic programming is an effective tool for creating efficient and elegant solutions to many programming problems, at least once you get over the shock of seeing code that violates many of the accepted rules of good programming. We have used metamorphosis for many years to solve problems in the logic-level simulation of VLSI circuits. These solutions have provided some spectacular gains in performance, inspiring us to look for metamorphic solutions to other problems. We have found metamorphic solutions to many problems including string searching, sorting, and depth first search, most of which provide performance gains over conventional coding. A few of these solutions are presented here. These programs violate the rules of good programming, but with a few minor compiler enhancements, our programming techniques become clean and well structured.

Date: 2005
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A Note on the Regular Representation

2007-02-05T14:20:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

A quick note to explain the regular representation of a group, as opposed to the standard representation. It is well known that any group can be viewed as a set of permutations. Multiplying every element of a group by the same thing permutes the elements of the group. This note shows how that fact is used to create the regular representation. This is explained -- quite badly -- in many different books. This note is meant as a clarification.

Date: 2/5/07

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Orders of Matrices and Sizes of General Linear Groups

2007-02-05T14:17:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

Looking at general linear groups to determine when it is possible to embed Sn in GLm(2) where n>m. S7, it appears, cannot be embedded in either GL5(2) or GL4(2).

Date: 2/5/07

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Linear permutations and Eigenpolynomials

2007-02-05T14:14:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

Two short notes, one about linear permutations in S7 generated by 3x3 matrices and one on the eigenpolynomials of 4x4 matrices. All over GF(2).

Date: 2/5/07

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An Analysis of the 3x3 Matrix Group B7

2007-02-05T05:32:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This document analyzes the 3x3 matrix group B7 (over GF(2)) as a subgroup of S7.

Date: 2/4/07

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An Analysis of the 3x3 Matrix Group B6

2007-02-05T05:32:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This document analyzes the 3x3 matrix group B6 (over GF(2)) as a subgroup of S7.

Date: 2/4/07

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An Analysis of the 3x3 Matrix Group B5

2007-02-05T05:30:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This document analyzes the 3x3 matrix group B5 (over GF(2)) as a subgroup of S7.

Date: 2/4/07

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An Analysis of the 3x3 Matrix Group B4

2007-02-05T05:29:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This document analyzes the 3x3 matrix group B4 (over GF(2)) as a subgroup of S7.

Date: 2/4/07

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An Analysis of the 3x3 Matrix Group B3

2007-02-05T05:26:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This document analyzes the 3x3 matrix group B3 (over GF(2)) as a subgroup of S7.

Date: 2/4/07

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An Analysis of the 3x3 Matrix Group B2

2007-02-05T05:25:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This document analyzes the 3x3 matrix group B2 (over GF(2)) as a subgroup of S7.

Date: 2/4/07

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An Analysis of the 3x3 Matrix Group B1

2007-02-05T05:24:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This document analyzes the 3x3 matrix group B1 (over GF(2)) as a subgroup of S7.

Date: 2/4/07

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An Analysis of the 3x3 Matrix Group A7

2007-02-05T05:21:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This document analyzes the 3x3 matrix group A7 (over GF(2)) as a subgroup of S7.

Date: 2/4/07

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An Analysis of the 3x3 Matrix Group A6

2007-02-05T05:21:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This document analyzes the 3x3 matrix group A6 (over GF(2)) as a subgroup of S7.

Date: 2/4/07

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An Analysis of the 3x3 Matrix Group A5

2007-02-05T05:20:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This document analyzes the 3x3 matrix group A5 (over GF(2)) as a subgroup of S7.

Date: 2/4/07

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An Analysis of the 3x3 Matrix Group A4

2007-02-05T05:19:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This document analyzes the 3x3 matrix group A4 (over GF(2)) as a subgroup of S7.

Date: 2/4/07

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An Analysis of the 3x3 Matrix Group A3

2007-02-05T05:18:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This document analyzes the 3x3 matrix group A3 (over GF(2)) as a subgroup of S7.

Date: 2/4/07

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An Analysis of the 3x3 Matrix Group A2

2007-02-05T05:15:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This document analyzes the 3x3 matrix group A2 (over GF(2)) as a subgroup of S7.

Date: 2/4/07

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An Analysis of the 3x3 matrix group A1

2007-02-05T05:06:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This document analyzes the 3x3 matrix group A1 (over GF(2)) as a subgroup of S7.

Date: 2/4/07

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A New Kind of Reduction

2007-02-04T20:04:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This report gives a new method of reducing matrices. In the traditional approach, a rectangle of zeros in the upper left is required. In this method, the zero locations can be distributed throughout the matrix. A 4x4 matrix is used as an example, but any matrix will do. To find an acceptable pattern, place a rectangle of zeros in the upper left, then rearrange the rows and columns in exactly the same way to distribute the zeros throughout the matrix. These zero-distributed matrices will be conjugate to existing forms of matrices using a permutation matrix as the conjugacy matrix.

Date: 2/4/07

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Constructing 4x4 representations from 3x3 representations

2007-02-04T20:00:00Z

Author: Peter M. Maurer

EMail: Peter_Maurer@Baylor.edu

Abstract:

This report shows how to generate 4x4 representations of S4 (over GF(2)) from 3x3 representations. A lot of brute force calculation is done, and I hope you're impressed by that, but I'm still seeking some fundamental insight that simplifies this matter.

Date: 2/4/07

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