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Workshop: MATH-AI: Toward Human-Level Mathematical Reasoning

Neural Combinatorial Logic Circuit Synthesis from Input-Output Examples

Peter Belcak · Roger Wattenhofer


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.

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