53,491 research outputs found
Generalized Totalizer Encoding for Pseudo-Boolean Constraints
Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are
used to model many real-world problems. A common approach to solve these
constraints is to encode them into a SAT formula. The runtime of the SAT solver
on such formula is sensitive to the manner in which the given pseudo-Boolean
constraints are encoded. In this paper, we propose generalized Totalizer
encoding (GTE), which is an arc-consistency preserving extension of the
Totalizer encoding to pseudo-Boolean constraints. Unlike some other encodings,
the number of auxiliary variables required for GTE does not depend on the
magnitudes of the coefficients. Instead, it depends on the number of distinct
combinations of these coefficients. We show the superiority of GTE with respect
to other encodings when large pseudo-Boolean constraints have low number of
distinct coefficients. Our experimental results also show that GTE remains
competitive even when the pseudo-Boolean constraints do not have this
characteristic.Comment: 10 pages, 2 figures, 2 tables. To be published in 21st International
Conference on Principles and Practice of Constraint Programming 201
Partial Weighted MaxSAT for Optimal Planning
Abstract. We consider the problem of computing optimal plans for proposi-tional planning problems with action costs. In the spirit of leveraging advances in general-purpose automated reasoning for that setting, we develop an approach that operates by solving a sequence of partial weighted MaxSAT problems, each of which corresponds to a step-bounded variant of the problem at hand. Our ap-proach is the first SAT-based system in which a proof of cost-optimality is ob-tained using a MaxSAT procedure. It is also the first system of this kind to incor-porate an admissible planning heuristic. We perform a detailed empirical eval-uation of our work using benchmarks from a number of International Planning Competitions.
On Different Strategies for Eliminating Redundant Actions from Plans
Satisficing planning engines are often able to generate plans in a reasonable time, however, plans are often far from optimal. Such plans often contain a high number of redundant actions, that are actions, which can be removed without affecting the validity of the plans. Existing approaches for determining and eliminating redundant actions work in polynomial time, however, do not guarantee eliminating the "best" set of redundant actions, since such a problem is NP-complete. We introduce an approach which encodes the problem of determining the "best" set of redundant actions (i.e. having the maximum total-cost) as a weighted MaxSAT problem. Moreover, we adapt the existing polynomial technique which greedily tries to eliminate an action and its dependants from the plan in order to eliminate more expensive redundant actions. The proposed approaches are empirically compared to existing approaches on plans generated by state-of-the-art planning engines on standard planning benchmark
Community Structure in Industrial SAT Instances
Modern SAT solvers have experienced a remarkable progress on solving
industrial instances. Most of the techniques have been developed after an
intensive experimental process. It is believed that these techniques exploit
the underlying structure of industrial instances. However, there are few works
trying to exactly characterize the main features of this structure.
The research community on complex networks has developed techniques of
analysis and algorithms to study real-world graphs that can be used by the SAT
community. Recently, there have been some attempts to analyze the structure of
industrial SAT instances in terms of complex networks, with the aim of
explaining the success of SAT solving techniques, and possibly improving them.
In this paper, inspired by the results on complex networks, we study the
community structure, or modularity, of industrial SAT instances. In a graph
with clear community structure, or high modularity, we can find a partition of
its nodes into communities such that most edges connect variables of the same
community. In our analysis, we represent SAT instances as graphs, and we show
that most application benchmarks are characterized by a high modularity. On the
contrary, random SAT instances are closer to the classical Erd\"os-R\'enyi
random graph model, where no structure can be observed. We also analyze how
this structure evolves by the effects of the execution of a CDCL SAT solver. In
particular, we use the community structure to detect that new clauses learned
by the solver during the search contribute to destroy the original structure of
the formula. This is, learned clauses tend to contain variables of distinct
communities
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