We present our anytime MaxSAT solver TT-Open-WBO-Inc, focusing on its evolution since the initial version that won both of the weighted incomplete tracks of MaxSAT Evaluation 2019 (MSE19). The solver’s MSE20 version claimed victory in these tracks at MSE20 and secured second place in both unweighted incomplete tracks. The major innovation in the MSE20 version was the integration of SAT-based local search. The contributions of this paper include: (1) Introducing a previously unpublished variant of the SAT-based local search algorithm Polosat, Polosat-OBV, applied by default already in the MSE20 version, and showing its superiority for weighted solving; (2) Describing and analyzing TT-Open-WBO-Inc’s unweighted component, not studied in previous work; (3) Demonstrating that integrating the local search algorithm SATLike into TT-Open-WBO-Inc as a preprocessor enables it to outperform the winners of MSE20 in all four incomplete tracks.
Recently, the proof system MICE for the model counting problem #SAT was introduced by Fichte, Hecher and Roland (SAT’22). As demonstrated by Fichte et al., the system MICE can be used for proof logging for state-of-the-art #SAT solvers. We perform a proof-complexity study of MICE. For this we first simplify the rules of MICE and obtain a calculus MIC E ′ that is polynomially equivalent to MICE. We then establish an exponential lower bound for the number of proof steps in MIC E ′ (and hence also in MICE) for a specific family of CNFs. We also explain a tight connection between MIC E ′ proofs and decision DNNFs.
We give an analogue of the Riis Complexity Gap Theorem for Quantified Boolean Formulas (QBFs). Every first-order sentence φ without finite models gives rise to a sequence of QBFs whose minimal refutations in tree-like QResolution are either of polynomial size (if φ has no models) or at least exponential in size (if φ has some infinite model). However, differently from the translations to propositional logic, the translation to QBF must be given additional structure in order for the polynomial upper bound to hold in treelike Q-Resolution. This extra structure is not needed in the system tree-like ∀Exp+Res, where we see the complexity gap on a natural translation to QBF.
OMTPlan is a Python platform for optimal planning in numeric domains via reductions to Satisfiability Modulo Theories (SMT) and Optimization Modulo Theories (OMT). Currently, OMTPlan supports the expressive power of PDDL2.1 level 2 and features procedures for both satisficing and optimal planning. OMTPlan provides an open, easy to extend, yet efficient implementation framework. These goals are achieved through a modular design and the extensive use of state-of-the-art systems for SMT/OMT solving.
We define a distance function on propositional formulas in CNF as a measure of non-isomorphism of formulas: the larger the distance between two formulas is, the further they are from being isomorphic. This distance induces a metric on isomorphism classes of formulas. We show how this distance can be used for SAT solving, namely for per-instance algorithm selection where there is a “portfolio” of SAT solvers and there is a “meta-solver” that chooses a solver from the portfolio for a given input formula.
