bit manipulation - Inferring simplest method to convert bit array 1 to bit array 2 -

consider set of bit arrays of length n. consider set of 1-to-1 functions map set set.

now select single function out of latter set. there algorithm find "minimal" method of implementing function? assume have access fundamental bit array operators such , or xor not , left , right bitshifts.

in case you're wondering, reason want because i'm writing algorithm convert z-curve ordering of bits hilbert-curve ordering of bits. current method make lookup table, bet there's better option.

as simple example, let's have truth table looks this:

00 -> 10 01 -> 01 10 -> 00 11 -> 11 

then should able infer that, given input bit string input, output bit string output (in java syntax)

output = ((~input) << 1) ^ input 

here's proof in case:

00 -> 11 -> 10 -> 10 01 -> 10 -> 00 -> 01 10 -> 01 -> 10 -> 00 11 -> 00 -> 00 -> 11