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 >>>

Jan Krajicek

The working conjecture from K'04 that there is a proof complexity generator hard for all

proof systems can be equivalently formulated (for p-time generators) without a reference to proof complexity notions

as follows:

\begin{itemize}

\item There exist a p-time function $g$ extending each input by one bit such that its ...
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