Extracting Boolean Function using Machine Learning
If you have an exhaustive list of all possible inputs, and the output for each, you already know the relationship between the input and output.  You don't need fancy machine learning.

If you want to explicitly write a formula for this relationship, it is easy to write a DNF formula (each clause corresponds to a single input-output pair, i.e., a single row in the truth table).  It's also easy to write a CNF formula, using a similar construction (each clause corresponds to a single input where the corresponding output is false).

If you want to find the minimal-length formula for this relationship, that is probably NP-hard (in fact it is "even harder" in some sense).  However there are heuristics.  Read about Karnaugh maps, Quine-McCluskey, the Espresso heuristic, and the fields of logic synthesis and circuit minimization.



I don't expect machine learning to perform better than existing methods.  Existing methods have a lot of intelligence built in, based on this specific problem.  ML methods wouldn't be able to benefit from any of that.

Ultimately, if you want to know whether some machine learning method performs better than standard methods, the only way to know for sure is to try it.  But I don't expect it to yield useful results, without new insights.