2,649 research outputs found
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
Learning to Reason: Leveraging Neural Networks for Approximate DNF Counting
Weighted model counting (WMC) has emerged as a prevalent approach for
probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF
counting (weighted #DNF) is a special case, where approximations with
probabilistic guarantees are obtained in O(nm), where n denotes the number of
variables, and m the number of clauses of the input DNF, but this is not
scalable in practice. In this paper, we propose a neural model counting
approach for weighted #DNF that combines approximate model counting with deep
learning, and accurately approximates model counts in linear time when width is
bounded. We conduct experiments to validate our method, and show that our model
learns and generalizes very well to large-scale #DNF instances.Comment: To appear in Proceedings of the Thirty-Fourth AAAI Conference on
Artificial Intelligence (AAAI-20). Code and data available at:
https://github.com/ralphabb/NeuralDNF
Community structure in industrial SAT instances
Modern SAT solvers have experienced a remarkable progress on solving industrial instances. It is believed that most of these successful techniques exploit the underlying structure of industrial instances. 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, 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. Representing SAT instances as graphs, we show that most application benchmarks are characterized by a high modularity. On the contrary, random SAT instances are closer to the classical Erdös-Rényi 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, and observe that new clauses learned by the solver during the search contribute to destroy the original structure of the formula. Motivated by this observation, we finally present an application that exploits the community structure to detect relevant learned clauses, and we show that detecting these clauses results in an improvement on the performance of the SAT solver. Empirically, we observe that this improves the performance of several SAT solvers on industrial SAT formulas, especially on satisfiable instances.Peer ReviewedPostprint (published version
Structure and Complexity in Planning with Unary Operators
Unary operator domains -- i.e., domains in which operators have a single
effect -- arise naturally in many control problems. In its most general form,
the problem of STRIPS planning in unary operator domains is known to be as hard
as the general STRIPS planning problem -- both are PSPACE-complete. However,
unary operator domains induce a natural structure, called the domain's causal
graph. This graph relates between the preconditions and effect of each domain
operator. Causal graphs were exploited by Williams and Nayak in order to
analyze plan generation for one of the controllers in NASA's Deep-Space One
spacecraft. There, they utilized the fact that when this graph is acyclic, a
serialization ordering over any subgoal can be obtained quickly. In this paper
we conduct a comprehensive study of the relationship between the structure of a
domain's causal graph and the complexity of planning in this domain. On the
positive side, we show that a non-trivial polynomial time plan generation
algorithm exists for domains whose causal graph induces a polytree with a
constant bound on its node indegree. On the negative side, we show that even
plan existence is hard when the graph is a directed-path singly connected DAG.
More generally, we show that the number of paths in the causal graph is closely
related to the complexity of planning in the associated domain. Finally we
relate our results to the question of complexity of planning with serializable
subgoals
Structure and Problem Hardness: Goal Asymmetry and DPLL Proofs in<br> SAT-Based Planning
In Verification and in (optimal) AI Planning, a successful method is to
formulate the application as boolean satisfiability (SAT), and solve it with
state-of-the-art DPLL-based procedures. There is a lack of understanding of why
this works so well. Focussing on the Planning context, we identify a form of
problem structure concerned with the symmetrical or asymmetrical nature of the
cost of achieving the individual planning goals. We quantify this sort of
structure with a simple numeric parameter called AsymRatio, ranging between 0
and 1. We run experiments in 10 benchmark domains from the International
Planning Competitions since 2000; we show that AsymRatio is a good indicator of
SAT solver performance in 8 of these domains. We then examine carefully crafted
synthetic planning domains that allow control of the amount of structure, and
that are clean enough for a rigorous analysis of the combinatorial search
space. The domains are parameterized by size, and by the amount of structure.
The CNFs we examine are unsatisfiable, encoding one planning step less than the
length of the optimal plan. We prove upper and lower bounds on the size of the
best possible DPLL refutations, under different settings of the amount of
structure, as a function of size. We also identify the best possible sets of
branching variables (backdoors). With minimum AsymRatio, we prove exponential
lower bounds, and identify minimal backdoors of size linear in the number of
variables. With maximum AsymRatio, we identify logarithmic DPLL refutations
(and backdoors), showing a doubly exponential gap between the two structural
extreme cases. The reasons for this behavior -- the proof arguments --
illuminate the prototypical patterns of structure causing the empirical
behavior observed in the competition benchmarks
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