Is there a non-deterministic version of the complexity class PP?
PP is defined as a probabilistic class and we don't normally think of nondeterministic versions of any of these classes (as far as I'm aware). In a sense probabilistic classes and nondeterministic ones are already on the same spectrum -- let me illustrate. We can define a language to be in PP if there's a randomized poly-time TM ("RPTM") that on a yes instance accepts with $&gt; 0.5$ probability and on a no instance accepts with $\leq 0.5$ probability. Similarly we can define a language to be in NP if there's a RPTM accepting yes-instances w.prob $&gt; 0$ and accepting no-instances w.prob $0$. (Convince yourself of this if you haven't before.) BPP corresponds to probability thresholds $\geq 2/3$ and $\leq 1/3$ while RP corresponds to $\geq 1/2$ and $0$.

So you see, PP can already be viewed as a "nondeterministic" version of P, but with different requirements as compared to NP.