Automatic test generation plays a crucial role in software quality assurance by helping developers efficiently detect bugs. Search-Based Software Testing (SBST) techniques are among the most widely studied approaches, relying on heuristic search to explore the test space. While effective, SBST tools frequently fail to cover certain branches, especially those requiring scenario-specific values or deeper semantic reasoning. Recently, Large Language Models (LLMs) have shown promise in alleviating these limitations by leveraging their code comprehension abilities to generate meaningful tests. However, despite these advances, LLM-based approaches still struggle to cover hard-to-cover branches, leaving many branches to be handled manually. We define hard-to-cover branches as those that (1) require complex object construction, where valid inputs must be built through multi-step processes involving interdependent objects and specific attribute values, or (2) involve intricate inter-procedural dependencies, where the outcome of a branch condition depends on the chained execution of several methods. Existing LLM-based techniques are not equipped to handle such challenges: they achieve relatively low compilation success rates and lack sufficient semantic guidance when only given the code of the target method and limited context.

To address these issues, we propose TELPA, a novel LLM-based test generation technique enhanced by program analysis. TELPA combines lightweight program analyses with LLM prompting to systematically guide test generation toward hard-to-cover branches. First, its object construction analysis collects method invocation sequences that lead to target methods, enabling the LLM to observe how valid complex objects are constructed in practice. Second, its branch dependency analysis identifies the methods involved in branch conditions and incorporates their code in a semantically meaningful order. This allows the LLM to reason about inter-procedural dependencies instead of being overwhelmed by irrelevant surrounding code. To ensure efficiency, TELPA is triggered only when lightweight SBST tools fail to improve coverage, and it integrates a feedback loop where counter-examples—previously ineffective tests—are added to prompts to guide the LLM toward unexplored solutions.

We conducted an extensive evaluation of TELPA on 27 open-source Python projects widely used in prior studies. Results show that TELPA consistently outperforms state-of-the-art SBST (Pynguin) and LLM-based test generation tools (CODAMOSA, CHATTESTER). On average, TELPA achieves 34.10%, 25.93%, and 21.10% higher branch coverage than these baselines, respectively, under the same testing time budget. An ablation study further confirms the contribution of each major component: both object construction analysis and branch dependency analysis indeed improve branch coverage, and counter-example feedback enhances both efficiency and diversity of generated tests. These findings demonstrate that integrating program analysis with LLM prompting is a promising direction for overcoming the long-standing challenge of covering hard-to-cover branches.