ALGO: Synthesizing Algorithmic Programs with LLM-Generated Oracle Verifiers

TL;DR

ALGO introduces a framework that uses LLM-generated oracles to guide and verify algorithmic program synthesis, significantly improving success rates over existing models.

Contribution

The paper presents a novel method for synthesizing algorithmic programs using LLM-generated oracles for guidance and verification, enhancing correctness and performance.

Findings

LLM-generated oracles are correct in 88% of cases

ALGO improves pass rates by 8x over Codex

ALGO achieves 2.6x better pass rate over CodeT

Abstract

Large language models (LLMs) excel at implementing code from functionality descriptions but struggle with algorithmic problems that require not only implementation but also identification of the suitable algorithm. Moreover, LLM-generated programs lack guaranteed correctness and require human verification. To address these challenges, we propose ALGO, a framework that synthesizes Algorithmic programs with LLM-Generated Oracles to guide the generation and verify their correctness. ALGO first generates a reference oracle by prompting an LLM to exhaustively enumerate all the combinations of relevant variables. This oracle is then utilized to guide an arbitrary search strategy in exploring the algorithm space and to verify the synthesized algorithms. Our study shows that the LLM-generated oracles are correct for 88% of the cases. With the oracles as verifiers, ALGO can be integrated with any existing code generation model in a model-agnostic manner to enhance its performance. Experiments show that when equipped with ALGO, we achieve an 8x better one-submission pass rate over the Codex model and a 2.6x better one-submission pass rate over CodeT, the current state-of-the-art model on CodeContests. We can also get 1.3x better pass rate over the ChatGPT Code Interpreter on unseen problems. The problem set we used for testing, the prompts we used, the verifier and solution programs, and the test cases generated by ALGO are available at https://github.com/zkx06111/ALGO.