Technical Reports

Metamorphosis, State Machines, and Object Oriented Design

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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Posted by Peter M Maurer at
5/31/2007 12:36 PM | View Comments (0) | Add Comment | Trackbacks (0)
A Note on the Regular Representation

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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2/5/2007 8:20 AM | View Comments (0) | Add Comment | Trackbacks (0)
Orders of Matrices and Sizes of General Linear Groups

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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2/5/2007 8:17 AM | View Comments (0) | Add Comment | Trackbacks (0)
Linear permutations and Eigenpolynomials

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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2/5/2007 8:14 AM | View Comments (0) | Add Comment | Trackbacks (0)
An Analysis of the 3x3 Matrix Group B6

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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Posted by Peter M Maurer at
2/4/2007 11:32 PM | View Comments (0) | Add Comment | Trackbacks (0)
An Analysis of the 3x3 Matrix Group B7

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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2/4/2007 11:32 PM | View Comments (0) | Add Comment | Trackbacks (0)
An Analysis of the 3x3 Matrix Group B5

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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2/4/2007 11:30 PM | View Comments (0) | Add Comment | Trackbacks (0)
An Analysis of the 3x3 Matrix Group B4

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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2/4/2007 11:29 PM | View Comments (0) | Add Comment | Trackbacks (0)
An Analysis of the 3x3 Matrix Group B3

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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Posted by Peter M Maurer at
2/4/2007 11:26 PM | View Comments (0) | Add Comment | Trackbacks (0)
An Analysis of the 3x3 Matrix Group B2

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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Posted by Peter M Maurer at
2/4/2007 11:25 PM | View Comments (0) | Add Comment | Trackbacks (0)