Oded Goldreich, Avi Wigderson

In the theory of pseudorandomness, potential (uniform) observers

are modeled as probabilistic polynomial-time machines.

In fact many of the central results in

that theory are proven via probabilistic polynomial-time reductions.

In this paper we show that analogous deterministic reductions

are unlikely to hold. We conclude that randomness ...
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Jan Krajicek

We study the diagonalization in the context of proof

complexity. We prove that at least one of the

following three conjectures is true:

1. There is a boolean function computable in E

that has circuit complexity $2^{\Omega(n)}$.

2. NP is not closed under the complement.

3. There is no ... more >>>

Alan Nash, Russell Impagliazzo, Jeff Remmel

Diagonalization is a powerful technique in recursion theory and in

computational complexity \cite{For00}. The limits of this technique are

not clear. On the one hand, many people argue that conflicting

relativizations mean a complexity question cannot be resolved using only

diagonalization. On the other hand, it is not clear that ...
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Harry Buhrman, Lance Fortnow, Rahul Santhanam

We show several unconditional lower bounds for exponential time classes

against polynomial time classes with advice, including:

\begin{enumerate}

\item For any constant $c$, $\NEXP \not \subseteq \P^{\NP[n^c]}/n^c$

\item For any constant $c$, $\MAEXP \not \subseteq \MA/n^c$

\item $\BPEXP \not \subseteq \BPP/n^{o(1)}$

\end{enumerate}

It was previously unknown even whether $\NEXP \subseteq ... more >>>

Dung Nguyen, Alan Selman

We investigate autoreducibility properties of complete sets for $\cNEXP$ under different polynomial reductions.

Specifically, we show under some polynomial reductions that there is are complete sets for

$\cNEXP$ that are not autoreducible. We obtain the following results:

- There is a $\reduction{p}{tt}$-complete set for $\cNEXP$ that is not $\reduction{p}{btt}$-autoreducible.

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Dmitry Itsykson, Alexander Knop, Dmitry Sokolov

We address a natural question in average-case complexity: does there exist a language $L$ such that for all easy distributions $D$ the distributional problem $(L, D)$ is easy on the average while there exists some more hard distribution $D'$ such that $(L, D')$ is hard on the average? We consider ... more >>>

Rahul Santhanam, Iddo Tzameret

We propose a diagonalization-based approach to several important questions in proof complexity. We illustrate this approach in the context of the algebraic proof system IPS and in the context of propositional proof systems more generally.

We give an explicit sequence of CNF formulas $\{\phi_n\}$ such that VNP$\neq$VP iff there are ... more >>>

Noga Alon, Olivier Bousquet, Kasper Green Larsen, Shay Moran, Shlomo Moran

We study several variants of a combinatorial game which is based on Cantor's diagonal argument. The game is between two players called Kronecker and Cantor. The names of the players are motivated by the known fact that Leopold Kronecker did not appreciate Georg Cantor's arguments about the infinite, and even ... more >>>