Automating algebraic proof systems is NP-hard

0543415 - MÚ 2022 RIV US eng C - Konferenční příspěvek (zahraniční konf.)
de Rezende, Susanna F. - Göös, M. - Nordström, J. - Pitassi, T. - Robere, R. - Sokolov, D.
Automating algebraic proof systems is NP-hard.
STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. New York: ACM, 2021 - (Khuller, S.; Vassilevska Williams, V.), s. 209-222. ISBN 978-1-4503-8053-9.
[53rd Annual ACM SIGACT Symposium on Theory of Computing. Virtual (IT), 21.06.2021-25.06.2021]
Institucionální podpora: RVO:67985840
Klíčová slova: proof complexity * automatability * pigeonhole principle * algebraic proof systems * lower bounds
Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
https://doi.org/10.1145/3406325.3451080

We show that algebraic proofs are hard to find: Given an unsatisfiable CNF formula F, it is NP-hard to find a refutation of F in the Nullstellensatz, Polynomial Calculus, or Sherali–Adams proof systems in time polynomial in the size of the shortest such refutation. Our work extends, and gives a simplified proof of, the recent breakthrough of Atserias and Müller (JACM 2020) that established an analogous result for Resolution.
Trvalý link: http://hdl.handle.net/11104/0320627