Orbits of Boolean functions Original Research Article

The group of congruences and permutations of the two-colored N-dimensional Boolean cube is considered. The total number of orbits generated by these automorphisms are shown to scale as 22n(2n+1N when N tends to infinity. The probability that a randomly chosen function will belong to an orbit containing the maximum possible number of elements, 2N+1N, approaches one as N goes to infinity. Simulations for N ⩽ 6 are in agreement with the scaling predictions.