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Circular Logic

Problem 209

Published on Friday, 19th September 2008, 06:00 pm; Solved by 1517

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
000
010
100
111
x y x XOR y
000
011
101
110

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)?