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Definition: $\mathcal P$-Computable and $\mathcal P$-Decidable Problems

Let $\mathcal P$ be a set of algorithms. A problem $P$ (respectively decision problem) is called $\mathcal P$-computable, (respectively $\mathcal P$-decidable) if there is an algorithm $\mathcal A \in \mathcal P$ such that $P$ can be computed (respectively decided), using $\mathcal A.$

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