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I think I heard in somewhere that it has been proven that $\mathsf{NP}$ is strictly contained in $\mathsf{EXP}$, that is $\mathsf{NP} \subsetneq \mathsf{EXP}$. Is this right? Wikipedia and book resources do not seem to bring me an answer..

I just found a post similar to this, but I am not sure whether $\mathsf{NP}$ is strictly contained in $\mathsf{EXP}$.

Raphael
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user2346
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1 Answers1

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Strictly contained means $\subsetneq$, i.e. it is the definition, it is not a result. So what you are saying is $$\mathsf{NP} \subsetneq \mathsf{ExpTime} \implies \mathsf{NP} \subsetneq \mathsf{ExpTime}$$ which is trivially true.

If you are asking if $\mathsf{NP}\subsetneq \mathsf{ExpTime} $ then the answer is: it is unknown.

You may want to check the Wikipedia article about Exponential Time Hypothesis which many experts believe is true.

Juho
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Kaveh
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