6 research outputs found
MaxSAT Resolution and Subcube Sums
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 proof system called
the SubCubeSums proof system. This system, which p-simulates MaxResW, can be
viewed as a special case of the semialgebraic 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
MaxSAT Evaluation 2018 : Solver and Benchmark Descriptions
Non peer reviewe
Equivalence Between Systems Stronger Than Resolution
In recent years there has been an increasing interest in studying proof systems stronger than Resolution, with the aim of building more efficient SAT solvers based on them. In defining these proof systems, we try to find a balance between the power of the proof system (the size of the proofs required to refute a formula) and the difficulty of finding the proofs. Among those proof systems we can mention Circular Resolution, MaxSAT Resolution with Extensions and MaxSAT Resolution with the Dual-Rail encoding.
In this paper we study the relative power of those proof systems from a theoretical perspective. We prove that Circular Resolution and MaxSAT Resolution with extension are polynomially equivalent proof systems. This result is generalized to arbitrary sets of inference rules with proof constructions based on circular graphs or based on weighted clauses. We also prove that when we restrict the Split rule (that both systems use) to bounded size clauses, these two restricted systems are also equivalent. Finally, we show the relationship between these two restricted systems and Dual-Rail MaxSAT Resolution.Research partially supported by the EU H2020 Research and Innovation Programme
under the LOGISTAR project (Grant Agreement No. 769142), the MINECO-FEDER
project TASSAT3 (TIN2016-76573-C2-2-P) and the MICINN project PROOFS
(PID2019-109137GB-C21)