MIP* = RE

@article{Ji2021MIPR,
  title={MIP* = RE},
  author={Zhengfeng Ji and Anand Natarajan and Thomas Vidick and John Wright and Henry S. Yuen},
  journal={Communications of the ACM},
  year={2021},
  volume={64},
  pages={131 - 138}
}
Note from the Research Highlights Co-Chairs: A Research Highlights paper appearing in Communications is usually peer-reviewed prior to publication. The following paper is unusual in that it is still under review. However, the result has generated enormous excitement in the research community, and came strongly nominated by SIGACT, a nomination seconded by external reviewers. The complexity class NP characterizes the collection of computational problems that have efficiently verifiable solutions… 

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On the complexity of zero gap MIP

This paper proves that $\mathsf{MIP}^*_0$ extends beyond the first level of the arithmetical hierarchy, and in fact is equal to $\Pi_2^0$, the class of languages that can be decided by quantified formulas of the form $\forall y \, \exists z \, R(x,y,z)$.
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