. Similarly,forfixeda(t) wealsodefine Losst(a(t);S,S0,α) def= Pr[At(a1,,at 1,S) = at ] Pr[At(a1,,at 1,S0) = at ]

Fix any (S,S0) S. In what follows, we takea(t) = (a1,...,at) to be distributed as the random output of adaptive composition applied toS0, that is a(t) A(t)(S0). A.4 ProofofTheorem4.5 Denote byAfiltt the subroutine given by thet-th step of the individual filtering algorithm; that is, at = Afiltt (a1,...,at 1,S).