I understand the logic minimization problem is NP-hard when given the onset, since the last step is equivalent to set cover optimization.
If instead we are given a partial truth table, and we just want to determine the minimal terms that fill in the missing values in the truth table, is this still NP-hard?
For example, the onset and missing value with three variables:
A B C X 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 ? 1 1 1 1
Is it still NP-hard to find the minimal term consistent with the onset that fills in the
I suspect it is still NP-hard, because if it were not NP-Hard to find the minimal term for one missing value, and we could find the minimal term in polynomial time with the number of items in the onset, then we could apply this algorithm to each item in the onset in polynomial time, and then combine all the terms to get the minimal expression, also in polynomial time.
I basically want to double check the above reasoning and make sure I did not miss anything.