What is Circuit completeness? Definition and why it matters
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A circuit is complete with respect to a specification if every input the specification allows has a satisfying witness, so an honest prover is never blocked from proving a true statement.

Detail: Completeness failures are availability bugs: a wallet that cannot spend, a bridge that cannot finalise, a rollup that cannot include a legitimate transaction. They are less discussed than soundness bugs because they do not lose funds directly, but they are common when constraints are tightened during a fix. A sound-and-complete theorem pins the circuit to its specification exactly, which is what allows untrusted optimisation, including by AI agents, without loss of correctness.

Source page: https://sorryfree.com/glossary/circuit-completeness/
Compiled by: sorryfree editors (https://sorryfree.com/about/)
Last reviewed: 2026-09-13