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Talk:Logical graph (view source)

Revision as of 22:18, 12 December 2008

9,280 bytes added ,  22:18, 12 December 2008
→‎Tables: redo beta table
Line 828: Line 828:  
| <math>\beta_{15}</math>
 
| <math>\beta_{15}</math>
 
|-
 
|-
−
| <math>f_0</math> || 0000 || <math>(~)</math>
+
| <math>f_0</math>
−
| 1   || 1   || 1   || 1   || 1   || 1   || 1   || 1
+
| 0000
−
| 1   || 1   || 1   || 1   || 1   || 1   || 1   || 1
+
| <math>(~)</math>
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_1</math> || 0001 || <math>(u)(v)\!</math>
+
| <math>f_1</math>
−
|&nbsp;|| 1   ||&nbsp;|| 1    ||&nbsp;|| 1    ||&nbsp;|| 1
+
| 0001
−
|&nbsp;|| 1   ||&nbsp;|| 1    ||&nbsp;|| 1    ||&nbsp;|| 1
+
| <math>(u)(v)\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_2</math> || 0010 || <math>(u) v\!</math>
+
| <math>f_2</math>
−
|&nbsp;||&nbsp;|| 1   || 1   ||&nbsp;||&nbsp;|| 1   || 1
+
| 0010
−
|&nbsp;||&nbsp;|| 1   || 1   ||&nbsp;||&nbsp;|| 1   || 1
+
| <math>(u) v\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_3</math> || 0011 || <math>(u)\!</math>
+
| <math>f_3</math>
−
|&nbsp;||&nbsp;||&nbsp;|| 1   ||&nbsp;||&nbsp;||&nbsp;|| 1
+
| 0011
−
|&nbsp;||&nbsp;||&nbsp;|| 1   ||&nbsp;||&nbsp;||&nbsp;|| 1
+
| <math>(u)\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_4</math> || 0100 || <math>u (v)\!</math>
+
| <math>f_4</math>
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 1   || 1   || 1   || 1
+
| 0100
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 1   || 1   || 1   || 1
+
| <math>u (v)\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_5</math> || 0101 || <math>(v)\!</math>
+
| <math>f_5</math>
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 1   ||&nbsp;|| 1
+
| 0101
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 1   ||&nbsp;|| 1
+
| <math>(v)\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_6</math> || 0110 || <math>(u, v)\!</math>
+
| <math>f_6</math>
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 1   || 1
+
| 0110
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 1   || 1
+
| <math>(u, v)\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_7</math> || 0111 || <math>(u v)\!</math>
+
| <math>f_7</math>
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 1
+
| 0111
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 1
+
| <math>(u v)\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_8</math> || 1000 || <math>u v\!</math>
+
| <math>f_8</math>
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
| 1000
−
| 1   || 1   || 1   || 1   || 1   || 1   || 1   || 1
+
| <math>u v\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_9</math> || 1001 || <math>((u, v))\!</math>
+
| <math>f_9</math>
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
| 1001
−
|&nbsp;|| 1   ||&nbsp;|| 1   ||&nbsp;|| 1    ||&nbsp;|| 1
+
| <math>((u, v))\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_{10}</math> || 1010 || <math>v\!</math>
+
| <math>f_{10}</math>
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
| 1010
−
|&nbsp;||&nbsp;|| 1   || 1   ||&nbsp;||&nbsp;|| 1   || 1
+
| <math>v\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_{11}</math> || 1011 || <math>(u (v))\!</math>
+
| <math>f_{11}</math>
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
| 1011
−
|&nbsp;||&nbsp;||&nbsp;|| 1   ||&nbsp;||&nbsp;||&nbsp;|| 1
+
| <math>(u (v))\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_{12}</math> || 1100 || <math>u\!</math>
+
| <math>f_{12}</math>
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
| 1100
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 1   || 1   || 1   || 1
+
| <math>u\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_{13}</math> || 1101 || <math>((u) v)\!</math>
+
| <math>f_{13}</math>
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
| 1101
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 1   ||&nbsp;|| 1
+
| <math>((u) v)\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_{14}</math> || 1110 || <math>((u)(y))\!</math>
+
| <math>f_{14}</math>
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
| 1110
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 1   || 1
+
| <math>((u)(y))\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 +
| style="background:black; color:white" | 1
 
|-
 
|-
−
| <math>f_{15}</math> || 1111 || <math>((~))\!</math>
+
| <math>f_{15}</math>
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;
+
| 1111
−
|&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;|| 1
+
| <math>((~))\!</math>
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:white; color:black" | 0
 +
| style="background:black; color:white" | 1
 
|}<br>
 
|}<br>
  
Jon Awbrey
12,080

edits

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