Optimal algorithms and proofs (Dagstuhl Seminar 14421)

This report documents the programme and the outcomes of the Dagstuhl Seminar 14421 "Optimal algorithms and proofs". The seminar brought together researchers working in computational and proof complexity, logic, and the theory of approximations. Each of these areas has its own, but connected notion of optimality; and the main aim of the seminar was to bring together researchers from these different areas, for an exchange of ideas, techniques, and open questions, thereby triggering new research collaborations across established research boundaries

A remark on pseudo proof systems and hard instances of the satisfiability problem

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 Krajícek. Pseudo proof systems are elements of a particular nonstandard model constructed by forcing with random variables. We show that the existence of mad pseudo proof systems is equivalent to the existence of a randomized polynomial time procedure with a highly restrictive use of randomness which produces satisfiable formulas whose satisfying assignments are probably hard to find.Peer ReviewedPostprint (published version

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum