Message passing for quantified Boolean formulas

We introduce two types of message passing algorithms for quantified Boolean formulas (QBF). The first type is a message passing based heuristics that can prove unsatisfiability of the QBF by assigning the universal variables in such a way that the remaining formula is unsatisfiable. In the second type, we use message passing to guide branching heuristics of a Davis-Putnam Logemann-Loveland (DPLL) complete solver. Numerical experiments show that on random QBFs our branching heuristics gives robust exponential efficiency gain with respect to the state-of-art solvers. We also manage to solve some previously unsolved benchmarks from the QBFLIB library. Apart from this our study sheds light on using message passing in small systems and as subroutines in complete solvers.Comment: 14 pages, 7 figure

Formula partitioning revisited

Dividing a Boolean formula into smaller independent sub-formulae can be a useful technique for accelerating the solution of Boolean problems, including SAT and #SAT. Nevertheless, and despite promising early results, formula partitioning is hardly used in state-of-the-art solvers. In this paper, we show that this is rooted in a lack of consistency of the usefulness of formula partitioning techniques. In particular, we evaluate two existing and a novel partitioning model, coupled with two existing and two novel partitioning algorithms, on a wide range of benchmark instances. Our results show that there is no one-size-fits-all solution: for different formula types, different partitioning models and algorithms are the most suitable. While these results might seem negative, they help to improve our understanding about formula partitioning; moreover, the findings also give guidance as to which method to use for what kinds of formulae

Anytime Computation of Cautious Consequences in Answer Set Programming

Query answering in Answer Set Programming (ASP) is usually solved by computing (a subset of) the cautious consequences of a logic program. This task is computationally very hard, and there are programs for which computing cautious consequences is not viable in reasonable time. However, current ASP solvers produce the (whole) set of cautious consequences only at the end of their computation. This paper reports on strategies for computing cautious consequences, also introducing anytime algorithms able to produce sound answers during the computation.Comment: To appear in Theory and Practice of Logic Programmin

Limit Crossing for Decision Problems

Limit crossing is a methodology in which modified versions of a problem are solved and compared, yielding useful information about the original problem. Pruning rules that are used to exclude portions of search trees are excellent examples of the limit-crossing technique. In our previous work, we examined limit crossing for optimization problems. In this paper, we extend this methodology to decision problems. We demonstrate the use of limit crossing in our design of a tool for identifying K-SAT backbones. This tool is guaranteed to identify all of the backbone variables by solving at most n+1 formulae, where n is the total number of variables. While previous 3-SAT backbone research was limited to 28 variables, we have computed backbones for 200 variables. In addition to being useful for identifying backbones, this code can be used directly to solve a special class of QBF problem

A Preference-Based Approach to Backbone Computation with Application to Argumentation

The backbone of a constraint satisfaction problem consists of those variables that take the same value in all solutions. Algorithms for determining the backbone of propositional formulas, i.e., Boolean satisfiability (SAT) instances, find various real-world applications. From the knowledge representation and reasoning (KRR) perspective, one interesting connection is that of backbones and the so-called ideal semantics in abstract argumentation. In this paper, we propose a new backbone algorithm which makes use of a "SAT with preferences" solver, i.e., a SAT solver which is guaranteed to output a most preferred satisfying assignment w.r.t. a given preference over literals of the SAT instance at hand. We also show empirically that the proposed approach is specifically effective in computing the ideal semantics of argumentation frameworks, noticeably outperforming an other state-of-the-art backbone solver as well as the winning approach of the recent ICCMA 2017 argumentation solver competition in the ideal semantics track.Peer reviewe