Formally, there are quite a few which are quite simple to show. For instance, for the string 'a', the shortest python problem which can produce this string is o

Formally, there are quite a few which are quite simple to show. For instance, for the string 'a', the shortest python problem which can produce this string is obviously print('a') since 'a' has only one character. Additionally, if you limit your language to a recursive language, you can compute complexity (which is no longer Komnogorov) directly. Simply begin enumerating all programs in order of length and then run them checking the output to see if it is that string. While this is by no means efficient, it works for recursive functions since they must halt. For Komogorov complexity, there isn't really a notion of inputs, merely that some particular string should be produced as output. For recursively enumerable (i.e. Turing complete) languages, the former method will not work because a program might run forever.