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No, LLVM does not generate Context-Free Grammar (CFG) directly. LLVM is a compiler infrastructure that provides a set of reusable libraries and tools for the development of compilers and related programming tools.

LLVM uses an intermediate representation (IR) known as LLVM IR that is generated from the input source code by frontend languages such as Clang (for C/C++) or Swift, among others. LLVM IR is a high-level, low-level virtual instruction set that is platform-independent and designed to facilitate optimization and analysis.

While LLVM IR can be thought of as a form of abstract syntax tree (AST) that represents the program structure, it is not a CFG in the traditional sense. It is a virtual assembly language that uses a single static assignment form (SSA) that provides a more structured representation of the program than generic ASTs, but it does not have the same level of precision that CFGs do.

However, it is possible to extract a CFG from LLVM IR through program analysis and transformations, such as through the use of the LLVM-based tool Clang's Control Flow Graph (CFG) Analysis, which generates a CFG based on LLVM IR for C and C++ source code.