I have seen this expression
What is the definition used here?
$\phi_x:{\Bbb N}_0^k\rightarrow {\Bbb N}_0$ is a total 0/1-valued function means that the domain of $\phi_x$ is ${\Bbb N}_0^k$ and the range is $\phi({\Bbb N}_0^k)\subseteq \{0,1\}$.
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$\phi_x:{\Bbb N}_0^k\rightarrow {\Bbb N}_0$ is a total 0/1-valued function means that the domain of $\phi_x$ is ${\Bbb N}_0^k$ and the range is $\phi({\Bbb N}_0^k)\subseteq \{0,1\}$.