18035076
On Subsumption Removal and On-the-Fly CNF Simplification
CNF Boolean formulas generated from resolution or solution enumeration often have much redundancy. Efficient algorithms are needed to simplify and compact such CNF formulas. In this paper, we present a novel algorithm to maintain a subsumption-free CNF clause database by efficiently detecting and removing subsumption as the clauses are being added. We then present an algorithm that compact CNF formula further by applying resolutions to make it Decremental Resolution Free. Our experimental evaluations show that these algorithms are efficient and effective in practice.
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.
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.
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.
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.
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.
4541399
Discriminant analysis with tensor representation
In this paper, we present a novel approach to solving the supervised dimensionality reduction problem by encoding an image object as a general tensor of 2nd or higher order. First, we propose a discriminant tensor criterion (DTC), whereby multiple interrelated lower-dimensional discriminative subspaces are derived for feature selection. Then, a novel approach called k-mode cluster-based discriminant analysis is presented to iteratively learn these subspaces by unfolding the tensor along different tensor dimensions. We call this algorithm discriminant analysis with tensor representation (DATER), which has the following characteristics: 1) multiple interrelated subspaces can collaborate to discriminate different classes; 2) for classification problems involving higher-order tensors, the DATER algorithm can avoid the curse of dimensionality dilemma and overcome the small sample size problem; and 3) the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in generalized eigenvalue decomposition. We provide extensive experiments by encoding face images as 2nd or 3rd order tensors to demonstrate that the proposed DATER algorithm based on higher order tensors has the potential to outperform the traditional subspace learning algorithms, especially in the small sample size cases.
37845872
The complexity of learning in PLN networks
Abstract In this paper, the complexity of learning in the feedforward PLN network is investigated by using Markov chain theory, when its training samples are incomplete (i.e., a network with hidden nodes). We present a learning algorithm. A formula for computing the average number of steps that the learning algorithm converges is obtained when the PLN network exists a solution. In the probabilistic sense, the completeness of the learning algorithm is proved. Some computer simulations are given to verify the analysis.
14488825
Image annotation using search and mining technologies
In this paper, we present a novel solution to the image annotation problem which annotates images using search and data mining technologies. An accurate keyword is required to initialize this process, and then leveraging a large-scale image database, it 1) searches for semantically and visually similar images, 2) and mines annotations from them. A notable advantage of this approach is that it enables unlimited vocabulary, while it is not possible for all existing approaches. Experimental results on real web images show the effectiveness and efficiency of the proposed algorithm.
12223354
Disjoint NP-pairs
We study the question of whether the class DisNP of disjoint pairs (A, B) of NP-sets contains a complete pair. The question relates to the question of whether optimal proof systems exist, and we relate it to the previously studied question of whether there exists a disjoint pair of NP-sets that is NP-hard. We show under reasonable hypotheses that nonsymmetric disjoint NP-pairs exist, which provide additional evidence for the existence of P-inseparable disjoint NP-pairs. We construct an oracle relative to which the class of disjoint NP-pairs does not have a complete pair, an oracle relative to which optimal proof systems exist, hence complete pairs exist, but no pair is NP-hard, and an oracle relative to which complete pairs exist, but optimal proof systems do not exist.
35154579
Incorporating priority scheme in IPv6 over ATM networks
An effective approach to support multiple QoS classes in IPv6 running over ATM networks is implemented by mapping the priority field of IPv6 into the ATM format. Such a scheme might not be necessary for simple congestion control in a network of equal capacity links, however, it might be important for multicasting to destinations reachable through a very diverse capacity network. When network congestion occurs, the cell loss requirements for different services can be satisfied by selectively discarding low priority cells. As the multi-priority scheme used in IPv6 is a ''differentiated service'' mechanism to enhance the QoS by best effort, its performance is certainly affected by the background traffic when these multi-priority traffic are multiplexed at the ATM level. This paper focuses on the performance with multi-priority scheme under different traffic conditions to determine the loss characteristics. The expected results are how QoS is affected and how priority can be given for more important traffic in the case of congested network.