You seem to have go it, the suggestion seems is to search all possible programs sorted by length.
"Start with the shortest program", a null instruction, which does not meet the criteria, "and complexity it iteratively" by appending new instruction in a breadth first manner "spanning a tree of all possible program."
You're correct that the first program that this search finds will satisfy K(X, T) but may not satisfy KT or kST.
"Start with the shortest program", a null instruction, which does not meet the criteria, "and complexity it iteratively" by appending new instruction in a breadth first manner "spanning a tree of all possible program."
You're correct that the first program that this search finds will satisfy K(X, T) but may not satisfy KT or kST.