Theory of Computing ------------------- Title : Round Complexity Versus Randomness Complexity in Interactive Proofs Authors : Maya Leshkowitz Volume : 18 Number : 13 Pages : 1-65 URL : https://theoryofcomputing.org/articles/v018a013 Abstract -------- Consider an interactive proof system for some set $S$ that has randomness complexity $r(n)$ for instances of length $n$, and arbitrary round complexity. We show a public coin interactive proof system for $S$ of round complexity $O(r(n)/\log r(n))$. Furthermore, the randomness complexity is preserved up to a constant factor, and the resulting interactive proof system has perfect completeness. ----------------- An extended abstract of this paper appeared in the Proceedings of the 22nd International Conference on Randomization and Computation (RANDOM'18).