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Communications of the ACM


Generating and Exploiting Automated Reasoning Proof Certificates

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Automated reasoning refers to a set of tools and techniques for automatically proving or disproving formulas in mathematical logic.35 It has many applications in computer science—for example, questions about the existence of bugs or security vulnerabilities in hardware or software systems can often be phrased as logical formulas, or verification conditions, whose validity can then be proved or disproved using automated reasoning techniques, a process known as formal verification.15,26 When successful, formal verification can guarantee freedom from certain kinds of design errors, an outcome that is otherwise extremely difficult to achieve. Driven by such potential benefits, the past couple of decades have seen a dramatic improvement in the performance and capabilities of automated reasoning tools, with a corresponding explosion of use cases, including formal verification, automated test-case generation, program analysis, program synthesis, and many more.5,37,38

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These applications rely crucially on automated reasoning tools producing correct results. However, ensuring correctness is a significant challenge. To meet the perpetual demand for better performance, automated reasoning tools have large and complex code bases, are highly optimized, and evolve rapidly, all of which puts their reliability at risk. While conventional software-engineering best practices can help, they are insufficient, especially when the goal is to provide incontrovertible mathematical guarantees. Formal verification of automated reasoning tools themselves requires an enormous effort and would have to be revisited every time the tools change. Fortunately, it is possible to provide strong correctness guarantees for an automated reasoner without having to trust the tool at all. The idea is to separate proof finding from proof checking. In contrast to the complex tools for finding proofs, automated proof checkers can be relatively simple (that is, a few thousand lines of code as opposed to a few hundred-thousand lines of code) and need only be revisited when the proof format changes, a relatively rare event. Because of their relative simplicity, proof checkers can also be vetted by the community when made open source. Even formal verification of simple proof checkers is not out of the question. It is also worth noting that proof checking can often be done offline, reducing the impact on performance.


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