We classify the univariate functions that are relativizable
closure properties of GapP, solving a problem posed by Hertrampf,
Vollmer, and Wagner (Structures '95). We also give a simple proof of
their classification of univariate functions that are relativizable
closure properties of #P.

Theoretical computer scientists have been debating the role of
oracles since the 1970's. This paper illustrates both that oracles
can give us nontrivial insights about the barrier problems in
circuit complexity, and that they need not prevent us from trying to
solve those problems.

First, we ... more >>>

Whether the class QMA (Quantum Merlin Arthur) is equal to QMA1, or QMA with one-sided error, has been an open problem for years. This note helps to explain why the problem is difficult, by using ideas from real analysis to give a "quantum oracle" relative to which QMA and QMA1 ... more >>>