Neural Combinatorial Logic Circuit Synthesis from Input-Output Examples

TL;DR

This paper introduces an explainable neural method for synthesizing combinatorial logic circuits from input-output examples, capable of handling incomplete data and generalizing to larger, practical circuits.

Contribution

It presents a novel neural approach that is fully explainable, adaptable to various logic atoms, and effective for synthesizing complex circuits including arithmetic and routing operations.

Findings

Successfully learns arithmetic, bitwise, and routing operations

Generalizes well to inductive scenarios with incomplete examples

Yields good results for practical circuit synthesis

Abstract

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.