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Circular Logic
Problem 209
Published on 19 September 2008 at 06:00 pm [Server Time]
A k-input binary truth table is a map from k input bits (binary digits, 0 [false] or 1 [true]) to 1 output bit. For example, the 2-input binary truth tables for the logical AND and XOR functions are:
| x | y | x AND y |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
| x | y | x XOR y |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
How many 6-input binary truth tables, τ, satisfy the formula
τ(a, b, c, d, e, f) AND τ(b, c, d, e, f, a XOR (b AND c)) = 0
for all 6-bit inputs (a, b, c, d, e, f)?
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