[Proof Complexity] Preprint - Pseudo proof systems and hard instances of SAT
Jan Maly
jmaly at dbai.tuwien.ac.at
Fri Feb 3 12:24:54 CET 2017
Dear all,
a preliminary version of my new paper with Moritz Muller, called "Pseudo
proof systems and hard instances of SAT", is available on my webpage:
http://www.dbai.tuwien.ac.at/staff/jmaly/. Please find the abstract
below and let us know if you have any comments.
All the best, Jan.
Abstract:
We link two concepts from the literature, namely hard sequences for the
satisfiability problem sat and so-called pseudo proof systems proposed
for study by Krajıcek. Pseudo proof systems are elements of a particular
nonstandard model constructed by forcing with random variables. Speaking
in standard terms, pseudo-proof systems are propositional proof systems
that are unsound in the sense that they might prove some falsifiable
propositional formulas but falsifying assignments are in a certain sense
hard to find. A hard sequence for a sat-algorithm is, roughly, a
feasibly computable sequence of satisfiable propositional formulas such
that the algorithm needs superpolynomial time on them. We show that the
existence of pseudo proof systems with a certain property that we call
madness is equivalent to the existence of so-called probably hard
sequences computable by certain randomized polynomial time algorithms.
We discuss variants of hard sequences and survey the relevant literature.
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