Supersimulators

ArXi:2509.17994v3 Announce Type: replace-cross We prove that every randomized Boolean function admits a supersimulator: a randomized polynomial-size circuit whose output on random inputs cannot be efficiently distinguished from reality with constant advantage, even by polynomially larger distinguishers. Our result builds on the landmark complexity-theoretic regularity lemma of Trevisan, Tulsiani and Vadhan, which, in contrast, provides a simulator that fools smaller distinguishers.