Collaborating Authors

Mitchell, David

An Experimental Study of Permanently Stored Learned Clauses Artificial Intelligence

Modern CDCL SAT solvers learn clauses rapidly, and an important heuristic is the clause deletion scheme. Most current solvers have two (or more) stores of clauses. One has ``valuable'' clauses which are never deleted. Most learned clauses are added to the other, with an aggressive deletion strategy to restrict its size. Recent solvers in the MapleSAT family, have comparatively complex deletion scheme, and perform well. Many solvers store only binary clauses permanently, but MapleLCMDistChronoBT stores clauses with small LBD permanently. We report an experimental study of the permanent clause store in MapleLCMDistChronoBT. We observe that this store can get quite large, but several methods for limiting its size reduced performance. We also show that alternate size and LBD based criteria improve performance, while still having large permanent stores. In particular, saving clauses up to size 8, and adding small numbers of high-centrality clauses, both improved performance, with the best improvement using both methods.

Propagators and Solvers for the Algebra of Modular Systems Artificial Intelligence

To appear in the proceedings of LPAR 21. Solving complex problems can involve non-trivial combinations of distinct knowledge bases and problem solvers. The Algebra of Modular Systems is a knowledge representation framework that provides a method for formally specifying such systems in purely semantic terms. Formally, an expression of the algebra defines a class of structures. Many expressive formalism used in practice solve the model expansion task, where a structure is given on the input and an expansion of this structure in the defined class of structures is searched (this practice overcomes the common undecidability problem for expressive logics). In this paper, we construct a solver for the model expansion task for a complex modular systems from an expression in the algebra and black-box propagators or solvers for the primitive modules. To this end, we define a general notion of propagators equipped with an explanation mechanism, an extension of the alge- bra to propagators, and a lazy conflict-driven learning algorithm. The result is a framework for seamlessly combining solving technology from different domains to produce a solver for a combined system.

Lifted Unit Propagation for Effective Grounding Artificial Intelligence

A grounding of a formula $\phi$ over a given finite domain is a ground formula which is equivalent to $\phi$ on that domain. Very effective propositional solvers have made grounding-based methods for problem solving increasingly important, however for realistic problem domains and instances, the size of groundings is often problematic. A key technique in ground (e.g., SAT) solvers is unit propagation, which often significantly reduces ground formula size even before search begins. We define a "lifted" version of unit propagation which may be carried out prior to grounding, and describe integration of the resulting technique into grounding algorithms. We describe an implementation of the method in a bottom-up grounder, and an experimental study of its performance.

Hard and Easy SAT Problems


"We report results from large-scale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satisfiability testing is quite difficult. Our results provide a benchmark for the evaluation of satisfiability-testing procedures." Proc. AAAI-92.

A New Method for Solving Hard Satisfiability Problems


"We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approaches such as the Davis-Putnam procedure or resolution. We also show that GSAT can solve structured satisfiability problems quickly. In particular, we solve encodings of graph coloring problems, N-queens, and Boolean induction. General application strategies and limitations of the approach are also discussed. GSAT is best viewed as a model-finding procedure. Its good performance suggests that it may be advantageous to reformulate reasoning tasks that have traditionally been viewed as theorem-proving problems as model-finding tasks." Proc. AAAI-92.