Thread Links Date Links
Thread Prev Thread Next Thread Index Date Prev Date Next Date Index

ONT Re: Differential Logic


o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

DLOG.  Note D74

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Transformations of Type B^2 -> B^2 (cont.)

Figure 61 shows how one might paint a picture of
the logical transformation F on the canvass that
was earlier primed for this purpose (way back in
Figure 30).

             o-----------------------------------------------------o
             | U                                                   |
             |                                                     |
             |            o-----------o   o-----------o            |
             |           /             \ /             \           |
             |          /               o               \          |
             |         /               / \               \         |
             |        /               /   \               \        |
             |       o               o     o               o       |
             |       |               |     |               |       |
             |       |       u       |     |       v       |       |
             |       |               |     |               |       |
             |       o               o     o               o       |
             |        \               \   /               /        |
             |         \               \ /               /         |
             |          \               o               /          |
             |           \             / \             /           |
             |            o-----------o   o-----------o            |
             |                                                     |
             |                                                     |
             o-----------------------------------------------------o
            / \                                                   / \
           /   \                                                 /   \
          /     \                                               /     \
         /       \                                             /       \
        /         \                                           /         \
       /           \                                         /           \
      /             \                                       /             \
     /               \                                     /               \
    /                 \                                   /                 \
   /                   \                                 /                   \
  /                     \                               /                     \
 /                       \                             /                       \
o-------------------------o                           o-------------------------o
| U                       |                           |\U \\\\\\\\\\\\\\\\\\\\\\|
|      o---o   o---o      |                           |\\\\\\o---o\\\o---o\\\\\\|
|     //////\ //////\     |                           |\\\\\/     \\/     \\\\\\|
|    ////////o///////\    |                           |\\\\/       o       \\\\\|
|   //////////\///////\   |                           |\\\/       /\\       \\\\|
|  o///////o///o///////o  |                           |\\o       o\\\o       o\\|
|  |// u //|///|// v //|  |                           |\\|   u   |\\\|   v   |\\|
|  o///////o///o///////o  |                           |\\o       o\\\o       o\\|
|   \///////\//////////   |                           |\\\\       \\/       /\\\|
|    \///////o////////    |                           |\\\\\       o       /\\\\|
|     \////// \//////     |                           |\\\\\\     /\\     /\\\\\|
|      o---o   o---o      |                           |\\\\\\o---o\\\o---o\\\\\\|
|                         |                           |\\\\\\\\\\\\\\\\\\\\\\\\\|
o-------------------------o                           o-------------------------o
 \                        |                           |                        /
   \                      |                           |                      /
     \                    |                           |                    /
       \        f         |                           |         g        /
         \                |                           |                /
           \              |                           |              /
             \            |                           |            /
               \          |                           |          /
                 \        |                           |        /
                   \      |                           |      /
             o-------\----|---------------------------|----/-------o
             | X       \  |                           |  /         |
             |           \|                           |/           |
             |            o-----------o   o-----------o            |
             |           //////////////\ /\\\\\\\\\\\\\\           |
             |          ////////////////o\\\\\\\\\\\\\\\\          |
             |         /////////////////X\\\\\\\\\\\\\\\\\         |
             |        /////////////////XXX\\\\\\\\\\\\\\\\\        |
             |       o///////////////oXXXXXo\\\\\\\\\\\\\\\o       |
             |       |///////////////|XXXXX|\\\\\\\\\\\\\\\|       |
             |       |////// x //////|XXXXX|\\\\\\ y \\\\\\|       |
             |       |///////////////|XXXXX|\\\\\\\\\\\\\\\|       |
             |       o///////////////oXXXXXo\\\\\\\\\\\\\\\o       |
             |        \///////////////\XXX/\\\\\\\\\\\\\\\/        |
             |         \///////////////\X/\\\\\\\\\\\\\\\/         |
             |          \///////////////o\\\\\\\\\\\\\\\/          |
             |           \////////////// \\\\\\\\\\\\\\/           |
             |            o-----------o   o-----------o            |
             |                                                     |
             |                                                     |
             o-----------------------------------------------------o
Figure 61.  A Propositional Transformation

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o