TY - GEN
T1 - MaxSAT Resolution and Subcube Sums
AU - Filmus, Yuval
AU - Mahajan, Meena
AU - Sood, Gaurav
AU - Vinyals, Marc
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - We study the MaxRes rule in the context of certifying unsatisfiability. We show that it can be exponentially more powerful than tree-like resolution, and when augmented with weakening (the system MaxResW), p-simulates tree-like resolution. In devising a lower bound technique specific to MaxRes (and not merely inheriting lower bounds from Res), we define a new semialgebraic proof system called the SubCubeSums proof system. This system, which p-simulates MaxResW, is a special case of the Sherali–Adams proof system. In expressivity, it is the integral restriction of conical juntas studied in the contexts of communication complexity and extension complexity. We show that it is not simulated by Res. Using a proof technique qualitatively different from the lower bounds that MaxResW inherits from Res, we show that Tseitin contradictions on expander graphs are hard to refute in SubCubeSums. We also establish a lower bound technique via lifting: for formulas requiring large degree in SubCubeSums, their XOR-ification requires large size in SubCubeSums.
AB - We study the MaxRes rule in the context of certifying unsatisfiability. We show that it can be exponentially more powerful than tree-like resolution, and when augmented with weakening (the system MaxResW), p-simulates tree-like resolution. In devising a lower bound technique specific to MaxRes (and not merely inheriting lower bounds from Res), we define a new semialgebraic proof system called the SubCubeSums proof system. This system, which p-simulates MaxResW, is a special case of the Sherali–Adams proof system. In expressivity, it is the integral restriction of conical juntas studied in the contexts of communication complexity and extension complexity. We show that it is not simulated by Res. Using a proof technique qualitatively different from the lower bounds that MaxResW inherits from Res, we show that Tseitin contradictions on expander graphs are hard to refute in SubCubeSums. We also establish a lower bound technique via lifting: for formulas requiring large degree in SubCubeSums, their XOR-ification requires large size in SubCubeSums.
KW - Conical juntas
KW - MaxSAT resolution
KW - Proof complexity
KW - Sherali–Adams proofs
KW - Subcube complexity
UR - http://www.scopus.com/inward/record.url?scp=85088278227&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-51825-7_21
DO - 10.1007/978-3-030-51825-7_21
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???
AN - SCOPUS:85088278227
SN - 9783030518240
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 295
EP - 311
BT - Theory and Applications of Satisfiability Testing – SAT 2020 - 23rd International Conference, Proceedings
A2 - Pulina, Luca
A2 - Seidl, Martina
T2 - 23rd International Conference on Theory and Applications of Satisfiability Testing, SAT 2020
Y2 - 3 July 2020 through 10 July 2020
ER -