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Whether or not backtracking is needed is really down to the grammar's ambiguity.

The auto-regressive nature of LLMs is actually something that counts against them, at least as some tell it. Although, really, the root problem is generating autoregressively from LLMs precludes planning ahead while also lacking any iterative refinement stage.

Backtracking, look-ahead, early failure pruning and staged generation are all very useful for fitting both concepts (refinement and planning ahead) in an auto-regressive generation framework.