I am trying to find indications that strengthen the conjecture of NEXP ⊊ EXP^NP.
Clearly NEXP ⊆ EXP^NP, and there are some hints that this inclusion is proper.
Some Examples: 1. A paper by Shuichi Hirahara: “Identifying an honest EXP^NP oracle among many”, which states that “No instance checker for EXP^NP -complete languages exists unless EXP^NP = NEXP” https://arxiv.org/abs/1502.07258
- A paper by Laszlo Babai, Lance Fortnow and Carsten Lund: “NON-DETERMINISTIC EXPONENTIAL TIME HAS TWO-PROVER INTERACTIVE PROTOCOLS” which states that we do not know whether NEXP provers are sufficient to prove any NEXP language to a verifier, but the best upper bound we know on the power of the provers for NEXP is EXP^NP http://people.cs.uchicago.edu/~fortnow/papers/mip2.pdf
Are there any additional known results on the conjecture of NEXP ⊊ EXP^NP? What are its implications on the separation of other classes?