A machine \(M\) is said to decide a language \(X\) just in case \(M\) computes the characteristic function of \(X\) relative to the standard input-output conventions for the model \(\mathfrak{M}\). For instance, a Turing machine \(T\)  decides \(X\) just in case for all \(x \in \{0,1\}^*\), the result of applying \(T\) to \(x\) yields a halting computation ending in a designated accept state if \(x \in X\) and a designated reject state if \(x \not\in X\). A function problem is that of computing the values of a given function \(f:A \rightarrow B\). \(M\) is said to solve a function problem \(f:A \rightarrow B\) just in case the mapping induced by its operation coincides with \(f(x)\) – i.e. if \(M(x) = f(x)\) for all \(x \in A\) where \(M(x)\) denotes the result of applying machine \(M\) to input \(x\), again relative to the input-output conventions for the model \(\mathfrak{M}\).