Formal Verification And Bitcoin

Forbes

23-05-2025

Bitcoin and Math
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Formal verification is one of the more theoretical areas of computer science. It relies on the tools of mathematical logic to verify whether statements are correct. This field historically has been obscure, but recent advances in AI may bring it front and center.
I spoke with Clark Barrett, a professor of computer science at Stanford, who tells of a software bug that once led to the explosion of a rocket. The software ran an instance that forced it to convert a floating-point number into an integer. This caused the program to crash and the rocket to explode. A formal verification of the code would have avoided that problem.
Compiling is the weakest form of verification. A stronger form would be to run a battery of test cases. To see this more clearly, consider a function that divides two numbers. Without doing any internal checks, that function could run on any numerical inputs. If your test cases excluded 0, your function would still compile. But the edge case of a 0 in the denominator would cause the program to crash. Only a formal verification would catch this because it's not sufficient just to evaluate the functions on the different inputs, but rather to assess the function on its underlying logic.
The bar for formal verification is high, and the tools are obscure and hard to use. Outside of the Mars rover, they have not had wide acceptance. But the one possible exception today is cloud services. Cloud providers allow customers to enter their own query logic when using their services. An error in the query logic, such as inadvertently typing 'or,' instead of 'and' can have existential consequences, giving everyone access instead of no one. As such, companies like AWS are now recruiting computer scientists in formal verification by the hundreds.
The big use case will be formally verifying code written by AI. As AI tools improve, more code will be written by AI, and we need fast and cheap ways to verify this code beyond simply compiling it. That's where formal verification could have its Super Bowl moment. There is now a big research effort underway to deploy these formal verification tools at scale to AI-generated code.
This could have an enormous impact, making software bugs a thing of the past. Not only would software be written faster with AI, but it would be better too.
Once these formal verification tools arrive, I'm eager to see how Bitcoin would fare. But the early answer here is that Bitcoin should fare well because it uses several strict forms of logic that give it its high security. For example, full nodes of the network check signatures (through SigOps) when verifying transactions. If the signature fails, the transaction will never enter the mempool, nor be included in a block. Similarly, miners win a block only if their hash of the block header lies below the difficulty target. And a transaction is valid only if the inputs exceeds its outputs.
In other words, the logic in Bitcoin is fully deterministic. There is no uncertainty about the rules of the protocol. And because of this, there is little room for software bugs, evidenced by the lack of hacks over the last 15 years.
That said, Bitcoin is still an example of social computing. You could say that it is technically vulnerable to collusion if, for example, every single miner in the world agreed to fork the chain. That could happen in theory. But that's where economics comes in: It would not be in the miner's interest to do so.