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Chapter 15 Algebraic Specication C: Lec 22 15.3 Permutation Voltages 15.4 Symmetric Graphs and Parallel Architectures 1 c 2010 by Jonathan L. Gross

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Page 1: Algebr aic Speci Þcation C: Lec 22 - Columbia University

Chapter 15Algebraic Specification C: Lec 22

15.3 Permutation Voltages15.4 Symmetric Graphs and Parallel Architectures

1 c 2010 by Jonathan L. Gross

Page 2: Algebr aic Speci Þcation C: Lec 22 - Columbia University

2 Chapter 15 Algebraic Specification C: Lec 22

15.3 PERMUTATION VOLTAGES

Permutation-Voltage Specifications

Figure 15.3.1

c 2010 by Jonathan L. Gross

Page 3: Algebr aic Speci Þcation C: Lec 22 - Columbia University

Section 15.3 Permutation Voltages 3

c 2010 by Jonathan L. Gross

Page 4: Algebr aic Speci Þcation C: Lec 22 - Columbia University

4 Chapter 15 Algebraic Specification C: Lec 22

c 2010 by Jonathan L. Gross

Page 5: Algebr aic Speci Þcation C: Lec 22 - Columbia University

Section 15.3 Permutation Voltages 5

c 2010 by Jonathan L. Gross

Page 6: Algebr aic Speci Þcation C: Lec 22 - Columbia University

6 Chapter 15 Algebraic Specification C: Lec 22

Drawing Graphs Specified by Perm Voltages

Figure 15.3.2

c 2010 by Jonathan L. Gross

Page 7: Algebr aic Speci Þcation C: Lec 22 - Columbia University

Section 15.3 Permutation Voltages 7

Figure 15.3.3

c 2010 by Jonathan L. Gross

Page 8: Algebr aic Speci Þcation C: Lec 22 - Columbia University

8 Chapter 15 Algebraic Specification C: Lec 22

Specifying the deBruijn Graphs

Fig 15.3.4

c 2010 by Jonathan L. Gross

Page 9: Algebr aic Speci Þcation C: Lec 22 - Columbia University

Section 15.3 Permutation Voltages 9

c 2010 by Jonathan L. Gross

Page 10: Algebr aic Speci Þcation C: Lec 22 - Columbia University

10 Chapter 15 Algebraic Specification C: Lec 22

Figure 15.3.5

c 2010 by Jonathan L. Gross

Page 11: Algebr aic Speci Þcation C: Lec 22 - Columbia University

Section 15.3 Permutation Voltages 11

Wreath Product

c 2010 by Jonathan L. Gross

Page 12: Algebr aic Speci Þcation C: Lec 22 - Columbia University

12 Chapter 15 Algebraic Specification C: Lec 22

15.4 SPECIFYING SYMMETRIC GRAPHS

Theoretical Criteria for Base Graphs

c 2010 by Jonathan L. Gross

Page 13: Algebr aic Speci Þcation C: Lec 22 - Columbia University

Section 15.4 Specifying Symmetric Graphs 13

c 2010 by Jonathan L. Gross

Page 14: Algebr aic Speci Þcation C: Lec 22 - Columbia University

14 Chapter 15 Algebraic Specification C: Lec 22

c 2010 by Jonathan L. Gross

Page 15: Algebr aic Speci Þcation C: Lec 22 - Columbia University

Section 15.4 Specifying Symmetric Graphs 15

Problems with Elementary Solutions

c 2010 by Jonathan L. Gross

Page 16: Algebr aic Speci Þcation C: Lec 22 - Columbia University

16 Chapter 15 Algebraic Specification C: Lec 22

c 2010 by Jonathan L. Gross

Page 17: Algebr aic Speci Þcation C: Lec 22 - Columbia University

Section 15.4 Specifying Symmetric Graphs 17

Figure 15.4.1

c 2010 by Jonathan L. Gross

Page 18: Algebr aic Speci Þcation C: Lec 22 - Columbia University

18 Chapter 15 Algebraic Specification C: Lec 22

c 2010 by Jonathan L. Gross

Page 19: Algebr aic Speci Þcation C: Lec 22 - Columbia University

Section 15.4 Specifying Symmetric Graphs 19

Fig 15.4.2

c 2010 by Jonathan L. Gross

Page 20: Algebr aic Speci Þcation C: Lec 22 - Columbia University

20 Chapter 15 Algebraic Specification C: Lec 22

Figure 15.4.3

c 2010 by Jonathan L. Gross

Page 21: Algebr aic Speci Þcation C: Lec 22 - Columbia University

Section 15.4 Specifying Symmetric Graphs 21

Fig 15.4.4

c 2010 by Jonathan L. Gross

Page 22: Algebr aic Speci Þcation C: Lec 22 - Columbia University

22 Chapter 15 Algebraic Specification C: Lec 22

c 2010 by Jonathan L. Gross

Page 23: Algebr aic Speci Þcation C: Lec 22 - Columbia University

Section 15.4 Specifying Symmetric Graphs 23

Problems with Complicated Solutions

Fig 15.4.5

c 2010 by Jonathan L. Gross

Page 24: Algebr aic Speci Þcation C: Lec 22 - Columbia University

24 Chapter 15 Algebraic Specification C: Lec 22

c 2010 by Jonathan L. Gross

Page 25: Algebr aic Speci Þcation C: Lec 22 - Columbia University

Section 15.4 Specifying Symmetric Graphs 25

Fig 15.4.6

Fig 15.4.7

c 2010 by Jonathan L. Gross

Page 26: Algebr aic Speci Þcation C: Lec 22 - Columbia University

26 Chapter 15 Algebraic Specification C: Lec 22

c 2010 by Jonathan L. Gross

Page 27: Algebr aic Speci Þcation C: Lec 22 - Columbia University

Section 15.4 Specifying Symmetric Graphs 27

Fig 15.4.8

Fig 15.4.9

c 2010 by Jonathan L. Gross

Page 28: Algebr aic Speci Þcation C: Lec 22 - Columbia University

28 Chapter 15 Algebraic Specification C: Lec 22

15.6 SUPPLEMENTARY EXERCISES

c 2010 by Jonathan L. Gross