Eric I. Hsu

Dsharp: fast d-DNNF compilation with sharpSAT

Knowledge compilation is a compelling technique for dealing with the intractability of propositional reasoning. One particularly effective target language is Deterministic Decomposable Negation Normal Form (d-DNNF). We exploit recent advances in #SAT solving in order to produce a new state-of-the-art CNF → d-DNNF compiler: Dsharp. Empirical results demonstrate that Dsharp is generally an order of magnitude faster than c2d, the de facto standard for compiling to d-DNNF, while yielding a representation of comparable size.

Probabilistically Estimating Backbones and Variable Bias: Experimental Overview

Backbone variables have the same assignment in all solutions to a given constraint satisfaction problem; more generally, biasrepresents the proportion of solutions that assign a variable a particular value. Intuitively such constructs would seem important to efficient search, but their study to date has been from a mostly conceptual perspective, in terms of indicating problem hardness or motivating and interpreting heuristics. Here we summarize a two-phase project where we first measure the ability of both existing and novel probabilistic message-passing techniques to directly estimate bias and identify backbones for the Boolean Satisfiability (SAT) Problem. We confirm that methods like Belief Propagation and Survey Propagation---plus Expectation Maximization-based variants---do produce good estimates with distinctive properties. The second phase demonstrates the use of bias estimation within a modern SAT solver, exhibiting a correlation between accurate, stable, estimates and successful backtracking search. The same process also yields a family of search heuristics that can dramatically improve search efficiency for the hard random problems considered.

Characterizing propagation methods for boolean satisfiability

Iterative algorithms such as Belief Propagation and Survey Propagation can handle some of the largest randomly-generated satisfiability problems (SAT) created to this point. But they can make inaccurate estimates or fail to converge on instances whose underlying constraint graphs contain small loops–a particularly strong concern with structured problems. More generally, their behavior is only well-understood in terms of statistical physics on a specific underlying model. Our alternative characterization of propagation algorithms presents them as value and variable ordering heuristics whose operation can be codified in terms of the Expectation Maximization (EM) method. Besides explaining failure to converge in the general case, understanding the equivalence between Propagation and EM yields new versions of such algorithms. When these are applied to SAT, such an understanding even yields a slight modification that guarantees convergence.

Preference-Based planning via MaxSAT

In this paper, we explore the application of partial weighted MaxSAT techniques for preference-based planning (PBP). To this end, we develop a compact partial weighted MaxSAT encoding for PBP based on the popular SAS+ planning formalism. Our encoding extends a SAS+ based encoding for SAT-based planning, SASE, to allow for the specification of simple preferences. To the best of our knowledge, the SAS+ formalism has never been exploited in the context of PBP. Our MaxSAT-based PBP planner, MSPlan, significantly outperformed the state-of-the-art STRIPS-based MaxSAT approach for PBP with respect to running time, solving more problems in a few cases. Interestingly, when compared to three state-of-the-art heuristic search planners for PBP, MSPlan consistently generated plans with comparable quality, slightly outperforming at least one of these three planners in almost every case. Our results illustrate the effectiveness of our SASE based encoding and suggests that MaxSAT-based PBP is a promising area of research.

VARSAT: Integrating Novel Probabilistic Inference Techniques with DPLL Search

Probabilistic inference techniques can be used to estimate variable bias , or the proportion of solutions to a given SAT problem that fix a variable positively or negatively. Methods like Belief Propagation (BP), Survey Propagation (SP), and Expectation Maximization BP (EMBP) have been used to guess solutions directly, but intuitively they should also prove useful as variable- and value- ordering heuristics within full backtracking (DPLL) search. Here we report on practical design issues for realizing this intuition in the VARSAT system, which is built upon the full-featured MiniSat solver. A second, algorithmic, contribution is to present four novel inference techniques that combine BP/SP models with local/global consistency constraints via the EMBP framework. Empirically, we can also report exponential speed-up over existing complete methods, for random problems at the critically-constrained phase transition region in problem hardness. For industrial problems, VARSAT is slower that MiniSat, but comparable in the number and types problems it is able to solve.