6734525
Propositional Satisfiability and Constraint Programming: A comparative survey
Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research cross-fertilizing occasionally. These two approaches to problem solving have a lot in common as evidenced by similar ideas underlying the branch and prune algorithms that are most successful at solving both kinds of problems. They also exhibit differences in the way they are used to state and solve problems since SAT's approach is, in general, a black-box approach, while CP aims at being tunable and programmable. This survey overviews the two areas in a comparative way, emphasizing the similarities and differences between the two and the points where we feel that one technology can benefit from ideas or experience acquired from the other.
11375306
A solver for quantified Boolean and linear constraints
We make a number of contributions to the understanding and practical resolution of quantified constraints. Unlike previous work in the CP literature that was essentially focused on constraints expressed as binary tables, we focus on Presburger Arithmetics, i.e., Boolean combinations of linear constraints. From a theoretical perspective, we clarify the problem of the treatment of universal quantifiers by proposing a "symmetric" version of the notion of quantified consistency. This notion imposes to maintain two constraint stores, which will be used to reason on universal and existential variables, respectively. We then describe a branch & bound algorithm that integrates both forms of propagation. Its implementation is, to the best of our knowledge, the first CP solver for this class of quantified constraints.
8920735
Partition-based decision heuristics for image computation using SAT and BDDs
Methods based on Boolean satisfiability (SAT) typically use a conjunctive normal form (CNF) representation of the Boolean formula, and exploit the structure of the given problem through use of various decision heuristics and implication methods. We propose a new decision heuristic based on separator-set induced partitioning of the underlying CNF graph. It targets those variables whose choice generates clause partitions with disjoint variable supports. This can potentially improve performance of SAT applications by decomposing the problem dynamically within the search. In the context of a recently proposed image computation method combining SAT and BDDs, this results in simpler BDD subproblems. We provide algorithms for CNF partitioning - one based on a clause-variable dependency matrix, and another based on standard hypergraph partitioning techniques, and also for the use of partitioning information in decision heuristics for SAT. The effectiveness of the proposed partition-based heuristic is shown with practical results for reachability analysis of benchmark sequential circuits.
14923930
Cache Performance of SAT Solvers: a Case Study for Efficient Implementation of Algorithms
We experimentally evaluate the cache performance of different SAT solvers as a case study for the efficient implementation of SAT algorithms. We evaluate several different Boolean Constraint Propagation (BCP) mechanisms and show their respective run time and cache performances on selected benchmark instances. From the experiments we conclude that a cache friendly data structure is a key element in the efficient implementation of SAT solvers. We also show empirical cache miss rates of several modern SAT solvers based on the Davis-Logemann-Loveland (DLL) algorithm with learning and non-chronological backtracking. We conclude that the recently developed SAT solvers are much more cache friendly in data structures and algorithm implementations compared with their predecessors.
70202123
The Quest for Efficient Boolean Satisfiability Solvers
The classical NP-complete problem of Boolean Satisfiability (SAT) has seen much interest in not just the theoretical computer science community, but also in areas where practical solutions to this problem enable significant practical applications. Since the first development of the basic search based algorithm proposed by Davis, Putnam, Logemann and Loveland (DPLL) about forty years ago, this area has seen active research effort with many interesting contributions that have culminated in state-of-the-art SAT solvers today being able to handle problem instances with thousands, and in same cases even millions, of variables. In this paper we examine some of the main ideas along this passage that have led to our current capabilities. Given the depth of the literature in this field, it is impossible to do this in any comprehensive way; rather we focus on techniques with consistent demonstrated efficiency in available solvers. For the most part, we focus on techniques within the basic DPLL search framework, but also briefly describe other approaches and look at some possible future research directions.
10515113
Validating SAT solvers using an independent resolution-based checker: practical implementations and other applications
As the use of SAT solvers as core engines in EDA applications grows, it becomes increasingly important to validate their correctness. In this paper, we describe the implementation of an independent resolution-based checking procedure that can check the validity of unsatisfiable claims produced by the SAT solver zchaff. We examine the practical implementation issues of such a checker and describe two implementations with different pros and cons. Experimental results show low overhead for the checking process. Our checker can work with many other modern SAT solvers with minor modifications, and it can provide information for debugging when checking fails. Finally we describe additional results that can be obtained by the validation process and briefly discuss their applications.
5888722
The transformation graph Gxyz when xyz=-++
The transformation graph G^-^+^+ of G is the graph with vertex set V(G)@?E(G) in which the vertex x and y are joined by an edge if one of the following conditions holds: (i) x,y@?V(G), and x and y are not adjacent in G, (ii) x,y@?E(G), and x and y are adjacent in G, (iii) one of x and y is in V(G) and the other is in E(G), and they are incident in G. In this paper, it is shown that for two graphs G and G^', G^-^+^+@?G^'^-^+^+ if and only if G@?G^'. Simple necessary and sufficient conditions are given for G^-^+^+ to be planar and hamiltonian, respectively. It is also shown that for a graph G, the edge-connectivity of G^-^+^+ is equal to its minimum degree. Two related conjectures and some research problems are presented.
22235359
Towards an Optimization-Based Method for Consolidating Domain Variabilities in Domain-Specific Web Services Composition
In this paper, we put forward an automatic method of acquiring the specific system composition model from a domain composition model and requirements for the specific system in domain-specific Web services composition. This is referred to as the variability consolidation problem in this paper. To achieve this goal, we designed a language to describe domain properties for Web services composition. The basis of our approach is to transform the domain composition model and the requirements for the specific system into a mathematical optimization problem, which can be solved by existing algorithms. Thus, this method is fully automatic and not prone to human errors. Our preliminary experimental results show that our method is quite feasible for solving problems with real world sizes.
5478794
Euclidean proximity and power diagrams
Power diagrams [Aur87] are a useful generalization of Voronoi diagrams in which the sites defining the diagram are not points but balls. They derive their name from the fact that the distance used in their definition is not the standard Euclidean distance, but instead the classical notion of the power of a point with respect to a ball [Cox61]. The advantage of the power distance is that the ‘bisector surfaces’, the surfaces equidistant from two given balls, are hyper-planes, and thus the Euclidean structure of these diagrams is polyhedral and they are easier to compute and manipulate than standard Voronoi diagrams. Several algorithms and applications for the power diagrams are already known, including those referenced in [IIM85, Aur88]. Most recently power diagrams have played a key role in work related to alpha shapes and ‘skins’ [Ede93, EM94, Ede95], as collections of balls are a natural model for molecular structures. The Voronoi diagram of point sites in any dimension has many useful proximity properties. Let us say that two sites are neighbors in the Voronoi diagram if their Voronoi cells share a common facet. It is well known that, for a set of points S, the closest pair of points in S are neighbors in the Voronoi diagram of S — equivalently, the closest pair of points must define an edge of the dual Delaunay diagram. Even more is true: the nearest neighbor to any point p ∈ S is a neighbor to p in the Voronoi diagram (equivalently, is connected to this neighbor by a Delaunay edge). Surprisingly, it seems that analogous proximity properties have not been studied for the power diagram. In this note, we consider the the power diagram of a set of disjoint balls. We show that the closest pair of
15844013
Survey of Disjoint NP-pairs and Relations to Propositional Proof Systems
We survey recent results on disjoint NP-pairs. In particular, we survey the relationship of disjoint NP-pairs to the theory of proof systems for propositional calculus.
1918361
Canny edge detection enhancement by scale multiplication
The technique of scale multiplication is analyzed in the framework of Canny edge detection. A scale multiplication function is defined as the product of the responses of the detection filter at two scales. Edge maps are constructed as the local maxima by thresholding the scale multiplication results. The detection and localization criteria of the scale multiplication are derived. At a small loss in the detection criterion, the localization criterion can be much improved by scale multiplication. The product of the two criteria for scale multiplication is greater than that for a single scale, which leads to better edge detection performance. Experimental results are presented.