Designing Predictable LLM-Verifier Systems for Formal Method Guarantee
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As researchers explore the uncharted territory where large language models (LLMs) meet formal verification, a lively debate unfolds around the potential of combining these two seemingly disparate approaches. Some commenters, like edwardtay, are thrilled by the prospect of harnessing formal verification to tackle LLMs' notorious unreliability, while others, such as XzAeRosho, probe the tricky question of bridging the semantic gap between LLMs' fuzzy logic and formal methods' precise specifications. A deeper dive into the paper reveals that the authors didn't actually use LLMs to write or verify code, prompting brantmv to wonder if the experiments were more simulated than real. The discussion takes a fascinating turn when jaggederest clarifies the meaning of "almost surely" in the context of probability, helping mapontosevenths appreciate the significance of being able to deterministically identify a halting state in code.
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A few thoughts:
1. What's the performance overhead? Formal verification is computationally expensive. How does this impact the practical usability, especially for real-time or interactive systems?
2. How do you handle the semantic gap? LLMs operate in natural language/fuzzy logic space, while formal methods require precise specifications. What's the translation layer like?
3. Are there domains where this works particularly well vs. poorly? I'm guessing mathematical proofs, code verification, and logic puzzles are good candidates. What about more subjective/creative tasks?
4. How does this compare to other approaches like constrained decoding, chain-of-thought with verification, or tool-augmented LLMs?
5. What's the failure mode? When the verifier rejects LLM output, how do you handle it? Regenerate? Provide feedback to the LLM?
This feels like it could be huge for safety-critical LLM applications. Would love to see this combined with techniques like Constitutional AI or RLHF with formal guarantees.
From what I understood, this validates the output correctness, not that the output aligns with the user goals, so there's still room for the LLM to get the user goals wrong, and this is only to validate the mathematical consistency between the output code and the formal specification (in this paper, within the ESBMC framework for C++ code).
So it's kind of tight scoped, in this case, but I think it points in the right direction for coding assistants, which usually get some language primitives wrong.
/? TLA LLM https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu... : 1 submission, ~20 comments
"AI will make formal verification go mainstream" (2025-12) https://news.ycombinator.com/item?id=46294574
Did I misread or miss something?
For those reasons, the grandiose name "LLM-Verifier Convergence Theorem" does not sit well with me.
"We prove that for any non-zero stage success probability, the system reaches the verified state almost surely"
What's the point if its still stochastic?
So like, imagine that you had some finite list of integers, and you were picking a random number from 0 to infinity - because the domain is infinite, any finite set has 0 probability, but that doesn't mean it doesn't exist.
https://en.wikipedia.org/wiki/Almost_surely
The ability to deterministcly identify that code eventually reaches a halting state, implies that we can use these stochastic tools to generate deterministic outcomes reliably in the future doesn't it?
Well, technically, no chance of failure. The chance of failure is absolute zero. Not close to zero, absolute zero. There will be no failure if the assumptions of the model are correct.
The real catch here is in the assumptions.
How long do you have before you need to have a solution? An hour, a year, a century? Too bad, almost sure convergence only provides a guarantee if you wait an infinite amount of time.
And then there's the question of the probability space you assume. (The sigma algebra.) Which things do you assume to have probability zero from the start and is that realistic?
Thanks for this. I was actually just thinking "this can't actually work, it would mean P vs NP is solved." Of course, this explains why it doesn't mean that.