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Paper:

TR22-120 | 24th August 2022 13:23

On the existence of strong proof complexity generators

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Abstract:

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 range $rng(g)$
intersects all infinite NP sets.
\end{itemize}
We consider several facets of this conjecture, including its links to bounded arithmetic (witnessing and
independence results) and the range avoidance problem,
to time-bounded Kolmogorov complexity, to feasible disjunction property of propositional proof
systems and to complexity of proof search.
We argue that a specific gadget generator from K'08 is a good candidate for $g$.


Comment(s):

Comment #1 to TR22-120 | 25th August 2022 10:58

A formulation

Authors: Jan Krajicek
Accepted on: 25th August 2022 10:58
Keywords: 


Comment:

The condition in the conjecture is supposed to mean:
|g(x)| = 1 + |x|.




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