  We propose a novel, fully explainable neural approach to synthesis of
combinatorial logic circuits from input-output examples. The carrying advantage
of our method is that it readily extends to inductive scenarios, where the set
of examples is incomplete but still indicative of the desired behaviour. Our
method can be employed for a virtually arbitrary choice of atoms - from logic
gates to FPGA blocks - as long as they can be formulated in a differentiable
fashion, and consistently yields good results for synthesis of practical
circuits of increasing size. In particular, we succeed in learning a number of
arithmetic, bitwise, and signal-routing operations, and even generalise towards
the correct behaviour in inductive scenarios. Our method, attacking a discrete
logical synthesis problem with an explainable neural approach, hints at a wider
promise for synthesis and reasoning-related tasks.
