Sound Acceptance Test

Definition

Sound Acceptance Test

A sound acceptance test for a predicate $P$ on a set $X$ is a sound algorithm

$$A:X\to \{\mathrm{yes},\perp \}$$

satisfying

$$\forall x\in X:A(x)=\mathrm{yes}⟹P(x).$$

Every accepted instance therefore satisfies $P$. The test may return $\perp$ for an instance that satisfies $P$; soundness excludes false acceptance, not inconclusive results.