# Are there complexity theory consequences of the collapse NEXP=EXP^NP?

It is clear that $$NEXP\subseteq EXP^{NP}$$, as a TM with exponential run time can simply query the NP oracle with an exponentially long query. However, it's not clear that the reverse $$EXP^{NP}\subseteq NEXP$$ is true. Are there any complexity theoretic conjectures which suggest this is not true and hence $$EXP^{NP}\not=NEXP$$?

• Isn't it the other way around? – M.Monet Mar 6 at 13:32
• I don’t really understand what do you expect to get. $\mathrm{EXP^{NP}\ne NEXP}$ is itself a complexity theoretic conjecture. This is implied, for example, by $\mathrm{NEXP\ne coNEXP}$. – Emil Jeřábek Mar 6 at 16:54
• @M.Monet Isn’t what the other way round? But if you mean the inclusions, they are stated correctly in the question: $\mathrm{NEXP\subseteq EXP^{NP}}$ is true, while $\mathrm{EXP^{NP}\subseteq NEXP}$ is likely false. – Emil Jeřábek Mar 6 at 16:57
• Oh yes sorry I read too fast. Should I delete the comments? – M.Monet Mar 6 at 17:39
• @user138901 - See my similar question here: cstheory.stackexchange.com/questions/41500/… There are many evidence that strengthen this conjecture, and I am still looking for more... – Avi Tal Mar 6 at 21:02