Visualizing a Non Deterministic Decider
For a nondeterministic decider the answer is At-least one &quot;copy&quot; halts on a &quot;yes&quot;/&quot;no&quot; state; copy-paste from another answer:

for a Nondeterministic Turing machine (NDTM) processing an input $x$ there can be infinite computations (paths); some of them will halt on the accept state $q_Y$, some will halt on the reject state $q_N$, some will run forever;

a string $x$ is accepted by a Nondeterministic Turing machine if at least one of its computations halts on the accepting state $q_Y$;

we say that &quot;$M$ accepts $x$ in $m$ steps&quot; if $M$ accepts $x$ and $m$ is the length of the shortest accepting computation on input $x$;

a language $L_M$ recognized by a NDTM $M$ is the set of $x$ accepted by $M$ (this is independent of whether $N$ is a decider or not);

the definition of time complexity for a Nondeterministic Turing Machine $M$ is slightly different from the definition of time complexity for a Deterministic Turing Machine:
$T_M(n) = max ( \{1\} \cup \{ m \; : \; $ there is an $x \in L_M$ such that   $|x|=n$ and $M$ accepts $x$ in $m$ steps $\})$

we say $M$ is a decider if $T_M(n)$ is computable.


See Garey&amp;Johnson, &quot;Computers and Intractability&quot;