PGS: Effective LLM Code Refinement via Property-Oriented and Structurally Minimal Feedback

Large Language Models (LLMs) excel at code generation, yet ensuring the functional correctness of their outputs remains a persistent challenge. Recent studies have applied Test-Driven Development (TDD) to refine code, leveraging execution feedback to guide the model toward correct solutions. However, such feedback is often noisy and uninformative, stemming from the scarcity of high-quality test cases and the abundance of noisy, auto-generated ones. In this work, we shift the focus from test-case generation to feedback quality. We introduce the Property-Generated Solver (PGS), a novel feedback-centric framework designed to generate highly effective feedback via two principles: it must provide semantic guidance beyond simple I/O mismatches through property validation, and be structurally minimal, to reduce cognitive load and isolate root causes. PGS operates by checking high-level program properties (e.g., a sorting function must produce a non-decreasing sequence) then providing the simplest failing counterexample to the LLM. This property-driven, minimal feedback steers LLMs toward correct and generalizable solutions. Across diverse benchmarks, PGS demonstrates superior performance, achieving a bug fix rate 1.4x-1.6x higher than the strongest debugging-based approaches and establishing a new state-of-the-art in automated code refinement.