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 ... more >>>

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 p-optimal ... more >>>

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 ... more >>>

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 >>>