If we have a TM $M$ to decide a language $L\in NP$, why can't we just simulate $M$ on a universal machine $M^c$ and return the opposite?
I've read on another thread here at MS that this isn't the definition of NDTM but I don't see why.
Can you clarify that for me?
By definition, a non-deterministic Turing machine M accepts a language $L$ if and only if any of the final states of $M$ when run with input $L$ are 'accepting states'. Running $M^c$ -- presumably, this is the same machine as $M$, but with reversed notion of which states are considered 'accepting' -- on some input will result in all final states being accepted if and only if the input is in $L^c$. Thus, this does not prove that $\mathrm{NP = co{-}NP}$, and there seems to be no easy way around this.