I am trying to understand if someone can apply an NTM to recognize a $coNP$ language.
From the definition we know that:
$NP$ - set of languages that can be recognized by NTM in polynomial time.
$coNP$ - set of all languages that are complement to $NP$ language.
as with $P$ vs. $NP$ question, we have $NP$ versus $coNP$ question.
Unfortunately, is not defined explicitly if can one recognize $coNP$ language with NTM.
However, if we take a look at few examples from the set of $coNP$ languages, few questions emerge.
$TAUTOLOGY$ = {$\varphi$: $\varphi$ is satisfied by every assignment}
$UNSAT$ = {$\varphi$: $\varphi$ is unsatisfiable}
These languages are known to be $coNP$ language and intuitively it seems like one can construct NTM to recognize these languages. On the other hand, if one can construct NTM to recognize them why them not in $NP$ class (by definition)? Maybe not all languages of $coNP$ can be solved by NTM, just few of them which are in $NP\cap coNP$. And if every language from $coNP$ class cannot be solved by NTM, does it mean that limitation of NTM is located in $coNP$. Does NTM have limitation at all?
I am a little bit confused, I would appreciate anyone that is willing to shine the light on this topic.