3,1

For n=5, computing the number of 3-CNF truth tables took 2^32 bytes and 2^38 iterations. Computing the same number for n=6 may require 2^64 bits and 2^71 iterations.

C. B. Barber, ttcnf 2005.1 (April 2005).

C. B. Barber, www.qhull.org/ttcnf.

The following program generates all truth tables of k-CNF expressions of n variables:

start with the truth table (2^2^n) - 1 //e.g., 0xFFFF for n=4

for each new truth table //e.g., 0xFFFF

for each (n choose k) variables //e.g., a, c, d

for each (2^k) clause of these variables //e.g., (a or not c or not d)

generate a truth table from the clause and previous truth table //e.g., NewTT = PrevTT and (...)

Bit operations allow an efficient implementation of the last step. If you represent each variable by its truth table, A, B, ..., in 1-CNF, then the last step is 'NewTT = PrevTT and (A or B or C ...)'. For example, with four variables a, b, c, and d, the 1-CNF truth table for 'a' is 0xFF00, 'not c' is 0x3333, and 'not d' is 0x5555. The corresponding step is 'NewTT = PrevTT and 0xFFBB'.

Cf. A109457, A112650, A000157, A000371, A000613, A000618, A003181.

Sequence in context: A017212 A018798 A017320 this_sequence A132637 A114850 A017440

Adjacent sequences: A112532 A112533 A112534 this_sequence A112536 A112537 A112538

bref,hard,nonn

C. Bradford Barber (bradb(AT)shore.net), Dec 13 2005