We give a meta-complexity characterization of EFI pairs, which are considered the ''minimal'' primitive in quantum cryptography (and are equivalent to quantum commitments). More precisely, we show that the existence of EFI pairs is equivalent to the following: there exists a non-uniformly samplable distribution over pure states such that the ... more >>>

A recent result of Ghentiyala, Li, and Stephens-Davidowitz (ECCC TR 25-210) shows that any language reducible to the Range Avoidance Problem (Avoid) via deterministic or randomized Turing reductions is contained in AM $\cap$ coAM. In this note, we present a different potential avenue for obtaining the same result via the ... more >>>

We study the power of negation in the Boolean and algebraic settings and show the following results.

* We construct a family of polynomials $P_n$ in $n$ variables, all of whose monomials have positive coefficients, such that $P_n$ can be computed by a depth three circuit of polynomial size ... more >>>