On the possibility of performing any multi-prover interactive proof in constantly many rounds

In 1990 Babai, Fortnow, and Lund built a two-prover interactive proof system for an $\operatorname{NEXP}$-complete set, thereby proving that the complexity classes $\operatorname{MIP}$ and $\operatorname{NEXP}$ coincide. In the present paper for an arbitrary $\operatorname{NEXP}$-set a two-prover interactive protocol is built with permissible error probability $1/3$, the number of rounds being bounded by a universal constant , i.e., it is proved that for some constant $c$ the classes $\operatorname{MIP}$ and $\operatorname{IP}(2,c)$ coincide.