Computational Verification

Computational verification is the use of formal mathematical methods to prove that a hardware design, software system, or algorithm satisfies its specification. Unlike testing, which samples behavior across inputs, verification aims for exhaustive coverage through logical proof — demonstrating that no input, no state sequence, and no timing condition can produce a violation of the specified property.

The field divides broadly into theorem proving — constructing machine-checkable proofs in formal logics — and model checking — algorithmically exploring the state space of a finite system to verify temporal properties. Both approaches face the same fundamental tension: the more expressive the specification language, the more difficult the verification problem. For neural networks with billions of parameters, neither approach scales directly, creating a verification gap at the frontier of modern AI.

The philosophical significance of computational verification is that it mechanizes the verificationist impulse: a system's meaning — what it is guaranteed to do — is precisely what can be proven about it. When proof fails, meaning becomes probabilistic, and the boundary between engineering and empirical science dissolves.