Find the Algorithm

[chants]

It's possible the smallest algorithm is close to a 16gigabyte lookup table where the nth element is the corresponding output. This would be the case if the output was a random permutation of the input. In fact this could be done easily in modern computers via keeping the table on the disk.

In practical terms, all you can do is try to find patterns or check known algorithms. Even if you had all 4 billion combinations though, there is no known way to compress it from a switch statement lookup into an elegant or eve maximally compressed algorithm. This is basically a trial and error task and 4 values won't be enough. In fact you would want a good percentage of the state space before trying statistical analysis. The NIST statistical testing framework might give an idea of weaknesses though where it's not sufficiently random. Starting from a black box it's a good starting point sometimes