I'm sorry, but differential describes pretty good what's happening here. Given a Query Q and a database instance I, we calculate a Result R
Q(I) = R
And indeed we derive some function D for the differential and are given a set of changes C where
D_Q(I)(C) = R' with Q(I+C)=R+R'
This D is clearly a differential function.
And if you look at the wikipedia entry for dynamic programming https://en.wikipedia.org/wiki/Dynamic_programming and indeed the important sentence "there is a relation between the value of the larger problem and the values of the sub-problems."
In this case here there is no splitting into sub-problems going on. We only have a function (the Query) and we calculate how the result changes when the input changes. If that's not a differential, I don't know what is.
Q(I) = R
And indeed we derive some function D for the differential and are given a set of changes C where
D_Q(I)(C) = R' with Q(I+C)=R+R'
This D is clearly a differential function.
And if you look at the wikipedia entry for dynamic programming https://en.wikipedia.org/wiki/Dynamic_programming and indeed the important sentence "there is a relation between the value of the larger problem and the values of the sub-problems."
In this case here there is no splitting into sub-problems going on. We only have a function (the Query) and we calculate how the result changes when the input changes. If that's not a differential, I don't know what is.