Richard Beigel

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.

Scott Aaronson

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 >>>

Scott Aaronson

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 >>>

Baris Aydinlioglu, Eric Bach

We strengthen existing evidence for the so-called "algebrization barrier". Algebrization --- short for algebraic relativization --- was introduced by Aaronson and Wigderson (AW) in order to characterize proofs involving arithmetization, simulation, and other "current techniques". However, unlike relativization, eligible statements under this notion do not seem to have basic closure ... more >>>

Hanlin Ren, Rahul Santhanam

Meta-complexity studies the complexity of computational problems about complexity theory, such as the Minimum Circuit Size Problem (MCSP) and its variants. We show that a relativization barrier applies to many important open questions in meta-complexity. We give relativized worlds where:

* MCSP can be solved in deterministic polynomial time, but ... more >>>

Shuichi Hirahara, Zhenjian Lu, Hanlin Ren

Relativization is one of the most fundamental concepts in complexity theory, which explains the difficulty of resolving major open problems. In this paper, we propose a weaker notion of relativization called *bounded relativization*. For a complexity class $C$, we say that a statement is *$C$-relativizing* if the statement holds relative ... more >>>