[Silasdev]

The idea is not to just generate any random string that matches the grammar. The idea is that if your request is "What are the first 10 digits of pi?" and you restrict the response to the regex: "[0-9]+\.[0-9]+", then you actually receive a correct answer of "3.1415926535" and not just a random string such as "1.2346789", which also happens to match the pattern.

[YeGoblynQueenne]

That will only work up to the point when the LLM can't generate a correct answer, whether conforming to a grammar or not. After that point, you'll just get grammatically correct bullshit.

Also, as noted in my reply to a sibling comment, grammars do not generate "any random string". That's the whole point of a grammar, that the generation is not random. For example it is perfectly feasible to write a grammar that completes a sentence with missing words, or continues some text etc.

And to be clear, it is entirely feasible to write a grammar that takes some string as input and generates a string as output that is a transformation of the input string satisfying some constraint. This kind of grammar is known as a transducer.

None of this should come as a surprise. Statistical language models are simply an alternative to knowledge-engineered grammars, used to do the same things that one can do with a grammar (except for the determinism). In a broad sense, a statistical language model is a kind of grammar, or perhaps it makes more sense to say that a grammar is a deterministic language model.