Phased synthesis of divide and conquer programs

We propose a fully automated method that takes as input an iterative or recursive reference implementation and produces divide-and-conquer implementations that are functionally equivalent to the input. Three interdependent components have to be synthesized: a function that divides the original problem instance, a function that solves each sub-instance, and a function that combines the results of sub-computations. We propose a methodology that splits the synthesis problem into three successive phases, each with a substantially reduced state space compared to the original monolithic task, and therefore substantially more tractable. Our methodology is implemented as an addition to the existing synthesis tool Parsynt, and we demonstrate the efficacy of it by synthesizing highly nontrivial divide-and-conquer implementations of a set of benchmarks fully automatically.