Integrating Conflict Driven Clause Learning to Local Search

This article introduces SatHyS (SAT HYbrid Solver), a novel hybrid approach for propositional satisfiability. It combines local search and conflict driven clause learning (CDCL) scheme. Each time the local search part reaches a local minimum, the CDCL is launched. For SAT problems it behaves like a tabu list, whereas for UNSAT ones, the CDCL part tries to focus on minimum unsatisfiable sub-formula (MUS). Experimental results show good performances on many classes of SAT instances from the last SAT competitions

Using Local Search to Find \MSSes and MUSes

International audienceIn this paper, a new complete technique to compute Maximal Satisfiable Subsets (MSSes) and Minimally Unsatisfiable Subformulas (MUSes) of sets of Boolean clauses is introduced. The approach improves the currently most efficient complete technique in several ways. It makes use of the powerful concept of critical clause and of a computationally inexpensive local search oracle to boost an exhaustive algorithm proposed by Liffiton and Sakallah. These features can allow exponential efficiency gains to be obtained. Accordingly, experimental studies show that this new approach outperforms the best current existing exhaustive ones

Analyzing and Extending an Infeasibility Analysis Algorithm

Constraint satisfaction problems (CSPs) involve finding assignments to a set of variables that satisfy some mathematical constraints. Unsatisfiable constraint problems are CSPs with no solution. However, useful characteristic subsets of these problems may be extracted with algorithms such as the MARCO algorithm, which outperforms the best known algorithms in the literature. A heuristic choice in the algorithm affects how it traverses the search space to output these subsets. This work analyzes the effect of this choice and introduces three improvements to the algorithm. The first of these improvements sacrifices completeness in terms of one type of subset in order to improve the output rate of another; the second and third are variations of a local search in between iterations of the algorithm which result in improved guidance in the search space. The performance of these improvements is analyzed both individually and in combinations across a variety of benchmarks and they are shown to improve the output rate of MARCO

Structure Functions of Unstable Lithium Isotopes

We study both the spin-average and spin-dependent structure functions of the lithium isotopes, $^{6-11}$Li, which could be measured at RIKEN and other nuclear facilities in the future. It is found that the light-cone momentum distribution of the valence neutron in the halo of $^{11}$Li is very sharp and symmetric around y = 1, because of the weak binding. The EMC ratios for Li isotopes are then calculated. We study the possibility of extracting the neutron structure function from data for the nuclear structure functions of the Li isotopes. Next we calculate the spin-dependent structure functions of $^{7,9,11}$Li isotopes, which have spin of 3/2. The effect of the nuclear binding and Fermi motion on the multipole spin structure function, $^{3/2}_{~1}g_1$, is about 10% in the region x < 0.7, but it becomes quite important at large x. The spin structure function of $^{3/2}_{~3}g_1$ is also investigated. Finally, we discuss the modification of the Gottfried and Bjorken integrals in a nuclear medium and point out several candidates for a pair of mirror nuclei to study the flavor-nonsinglet quark distributions in nuclei.Comment: 23 pages + 7 tables + 15 figure

Core-guided minimal correction set and core enumeration

A set of constraints is unsatisfiable if there is no solution that satisfies these constraints. To analyse unsatisfiable problems, the user needs to understand where inconsistencies come from and how they can be repaired. Minimal unsatisfiable cores and correction sets are important subsets of constraints that enable such analysis. In this work, we propose a new algorithm for extracting minimal unsatisfiable cores and correction sets simultaneously. Building on top of the relaxation and strengthening framework, we introduce novel techniques for extracting these sets. Our new solver significantly outperforms several state of the art algorithms on common benchmarks when it comes to extracting correction sets and compares favorably on core extraction.Peer ReviewedPostprint (published version

Improving MCS Enumeration via Caching

Enumeration of minimal correction sets (MCSes) of conjunctive normal form formulas is a central and highly intractable problem in infeasibility analysis of constraint systems. Often complete enumeration of MCSes is impossible due to both high computational cost and worst-case exponential number of MCSes. In such cases partial enumeration is sought for, finding applications in various domains, including axiom pinpointing in description logics among others. In this work we propose caching as a means of further improving the practical efficiency of current MCS enumeration approaches, and show the potential of caching via an empirical evaluation.Peer reviewe