Exact correctness for promise tasks

For a decision task $(Y,N)$ from QA task and promise domain, a solver is exact if its normalized output law assigns probability one to yes on every encoded $z\in Y$ and probability one to no on every encoded $z\in N$. For a search task $(D,R)$ from the same definition, it is exact if, for every encoded $z\in D$, its normalized output law assigns probability one to outputs $w$ satisfying $(z,w)\in R$. These are per-instance requirements; no correctness is asserted outside the promise.

The solver is one of the quantum algorithms in Quantum query algorithm or classical algorithms in Classical query algorithm. For a quantum solver, its output weights are the normalized finite-branch law of Normalized output law for finite quantum query branches. For a randomized classical solver, they are the probabilities induced by its declared finite random-tape law. Exactness does not follow merely from a circuit or algorithm description; it is a condition on its output law.