Synthesizing Efficient Memoization Algorithms

In this paper, we propose an automated approach to finding correct and efficient memoization algorithms from a given declarative specification. This problem has two major challenges: (i) a memoization algorithm is too large to be handled by conventional program synthesizers; (ii) we need to guarantee the efficiency of the memoization algorithm. To address this challenge, we structure the synthesis of memoization algorithms by introducing the local objective function and the memoization partition function and reduce the synthesis task to two smaller independent program synthesis tasks. Moreover, the number of distinct outputs of the function synthesized in the second synthesis task also decides the efficiency of the synthesized memoization algorithm, and we only need to minimize the number of different output values of the synthesized function. However, the generated synthesis task is still too complex for existing synthesizers. Thus, we propose a novel synthesis algorithm that combines the deductive and inductive methods to solve these tasks. To evaluate our algorithm, we collect 42 real-world benchmarks from Leetcode, the National Olympiad in Informatics in Provinces-Junior (a national-wide algorithmic programming contest in China), and previous approaches. Our approach successfully synhesizes 39/42 problems in a reasonable time, outperforming the baselines.