What are currently known methods of logic formula synthesis?

Question

Suppose our goal is to produce logic function, which transforms input binary data (some input variable assignments) into one output (true or false). The only information that is known is dataset of example inputs and outputs. What are some known approaches to synthesize such boolean function/expression which maps each inputs to desired output? For few variables this is easy task, but what about hundreds of variables and only partially provided dataset?

Answer 1

First: If you only have examples of input and output, i.e. you do not have a complete picture of the input-output mapping (a partially provided dataset as you say) then obviously you cannot expect to obtain a perfect function ... rather, you'll have to make an educated guess as to what the output should be for those inputs that are not in your example set.

For such generalizations, there are various machine learning approaches, and within that class of approaches, many like to use neural networks.