Checkerboard, Commutative Design Framework
Switch Block Design Problem
Given:
- length 4 wires + checkerboard = 8x8 grid
Consider all possible two-turn paths:
- 8 choose 2 = 28 pairs of paths to same output
- 7 possible output rows
- 6 types of two-point turns
- 6 x 7 x 28 = 1176 pairs of canonical expressions
- note: without checkerboard, only 6 x 3 x 6 = 108 pairs
more pairs => greater diversity potential
Find:
- mapping functions f, g for two switch blocks
Goal:
- choose f, g for maximum diversity,
such that each pair
of canonical expressions maps to a different track
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