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Static analysis is essential for program optimization, bug detection, and debugging, but its reliance on compilation and limited customization hampers practical use. Advances in LLMs enable a new paradigm of compilation-free, customizable analysis via prompting. LLMs excel in interpreting program semantics on small code snippets and allow users to define analysis tasks in natural language with few-shot examples. However, misalignment with program semantics can cause hallucinations, especially in sophisticated semantic analysis upon lengthy code snippets. We propose LLMSA, a compositional neuro-symbolic approach for compilation-free, customizable static analysis with reduced hallucinations. Specifically, we propose an analysis policy language to support users decomposing an analysis problem into several sub-problems that target simple syntactic or semantic properties upon smaller code snippets. The problem decomposition enables the LLMs to target more manageable semantic-related sub-problems, while the syntactic ones are resolved by parsing-based analysis without hallucinations. An analysis policy is evaluated with lazy, incremental, and parallel prompting, which mitigates the hallucinations and improves the performance. It is shown that LLMSA achieves comparable and even superior performance to existing techniques in various clients. For instance, it attains 66.27% precision and 78.57% recall in taint vulnerability detection, surpassing an industrial approach in F1 score by 0.20.