Shadows under the word-subword relation

We introduce a minimal shadow problem for a word-subword relation. We obtain upper and lower bounds for the minimal shadow cardinality.     

MEER—An EER model enhanced with structure methods

Entity relationship (ER) schemas include cardinality constraints, that restrict the dependencies among entities within a relationship type. The cardinality constraints have direct impact on the application maintenance, since insertions or deletions of entities or relationships might affect related entities. Indeed, maintenance of a system or of a database can be strengthened to enforce consistency with respect to the cardinality constraints in a schema. Yet, once an ER schema is translated into a logical database schema, or translated within a system, the direct correlation between the cardinality constraints and maintenance transactions is lost, since the components of the ER schema might be decomposed among those of the logical database schema or the target system.In this paper, a full solution to the enforcement of cardinality constraints in EER schemas is given. We extend the enhanced ER (EER) data model with structure-based update methods that are fully defined by the cardinality constraints. The structure methods are provably terminating and cardinality faithful, i.e., they do not insert new inconsistencies and can only decrease existing ones. A refined approach towards measuring the cardinality consistency of a database is introduced. The contribution of this paper is in the automatic creation of update methods, and in building the formal basis for proving their correctness.     

一个BCNF的多项式时间判定算法

文中指出了文献「１」中对ＢＣＮＦ判定问题证明过程的错之处，通过分析属于ＢＣＮＦ的关系模式的结构特点，给出了一个判定关系模式否属于ＢＮＣＦ的多项式时间算法。     

Well-known bound for the VC-dimension made easy

The Sauer lemma gives an upper bound for the cardinality of a set with given Vapnik-Chervonenkis dimension (VC-dimension). This paper presents a simple algebraic proof.     

The Linear Arrangement Problem Parameterized Above Guaranteed Value

A linear arrangement (LA) is an assignment of distinct integers to the vertices of a graph. The cost of an LA is the sum of lengths of the edges of the graph, where the length of an edge is defined as the absolute value of the difference of the integers assigned to its ends. For many application one hopes to find an LA with small cost. However, it is a classical NP-complete problem to decide whether a given graph G admits an LA of cost bounded by a given integer. Since every edge of G contributes at least one to the cost of any LA, the problem becomes trivially fixed-parameter tractable (FPT) if parameterized by the upper bound of the cost. Fernau asked whether the problem remains FPT if parameterized by the upper bound of the cost minus the number of edges of the given graph; thus whether the problem is FPT "parameterized above guaranteed value." We answer this question positively by deriving an algorithm which decides in time O(m + n + 5.88^k) whether a given graph with m edges and n vertices admits an LA of cost at most m + k (the algorithm computes such an LA if it exists). Our algorithm is based on a procedure which generates a problem kernel of linear size in linear time for a connected graph G. We also prove that more general parameterized LA problems stated by Serna and Thilikos are not FPT, unless P = NP.     

Worst-case/deterministic identification in H∞: the continuous-time case

Results obtained by the authors (1991) worst-case/deterministic H_∞ identification of discrete-time plants are extended to continuous-time plants. The problem involves identification of the transfer function of a stable strictly proper continuous-time plant from a finite number of noisy point samples of the plant frequency response. The assumed information consists of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, an upper bound on the roll-off rate of the plant, and an upper bound on the noise level. Concrete plans of identification algorithms are provided for this problem. Explicit worst-case/deterministic error bounds for each algorithm establish that they are robustly convergent and (essentially) asymptotically optimal. Additionally, these bounds provide an a priori computable H_∞ uncertainty specification, corresponding to the resulting identified plant transfer function, as an explicit function of the plant and noise prior information and the data cardinality     

On the restricted connectivity of the arrangement graph

We derive a general upper bound of the \(R_h\) -restricted connectivity for the arrangement graph, namely the minimum cardinality of a vertex set, whose removal disconnects the graph, but every remaining vertex has at least \(h ({\ge }0)\) neighbors in the survival graph. We show that this upper bound is exact when \(h \in [0, 2]\) and provide an asymptotic lower bound for the cases where \(h\ge 3\).     

Computing the Hausdorff distance between two B-spline curves

This paper presents a geometric pruning method for computing the Hausdorff distance between two B-spline curves. It presents a heuristic method for obtaining the one-sided Hausdorff distance in some interval as a lower bound of the Hausdorff distance, which is also possibly the exact Hausdorff distance. Then, an estimation of the upper bound of the Hausdorff distance in an sub-interval is given, which is used to eliminate the sub-intervals whose upper bounds are smaller than the present lower bound. The conditions whether the Hausdorff distance occurs at an end point of the two curves are also provided. These conditions are used to turn the Hausdorff distance computation problem between two curves into a minimum or maximum distance computation problem between a point and a curve, which can be solved well. A pruning technique based on several other elimination criteria is utilized to improve the efficiency of the new method. Numerical examples illustrate the efficiency and the robustness of the new method.     

关系模式一种基于超图的全部候选关键字求法

本文详细讨论了基于超图的关系模式的有关候选关键字的某些理论,给出了相应的定理.圆满地解决了关系模式全部候选关键字的求解问题,具体地给出了以递归形式的求全部候选关键字的新算法.     

无证书离线电子现金方案

在联盟结构生成过程中,同势的2个联盟通常具有相同值或相似值。在同势同值情况下建立不同联盟的限界时,必须搜索势结构图的最底两层。研究最优势结构生成问题,提出一种给定限界的势结构生成算法,确定需要进一步搜索的势结构。分析结果表明,搜索势结构图的最底两层和顶层后,通过搜索势结构集合,可以得到符合要求的限界。与其他势结构生成算法相比,该算法需要搜索的势结构数最少。     

给定限界的势结构生成算法

在联盟结构生成过程中,同势的2个联盟通常具有相同值或相似值。在同势同值情况下建立不同联盟的限界时,必须搜索势结构图的最底两层。研究最优势结构生成问题,提出一种给定限界的势结构生成算法,确定需要进一步搜索的势结构。分析结果表明,搜索势结构图的最底两层和顶层后,通过搜索势结构集合,可以得到符合要求的限界。与其他势结构生成算法相比,该算法需要搜索的势结构数最少。     

On the fuzzy cardinality of a fuzzy set

We look at problem of determining the number of elements of a fuzzy set and its cardinality. It is noted that the simple adding of membership grades often does not lead to a satisfactory results. We investigate the use of a fuzzy subset of the non-negative integers to represent the cardinality of a fuzzy set. We prove a fundamental relationship between the degree of fuzziness of a set A and the specificity of the fuzzy subset representing its cardinality. The problem of determining whether the cardinality of a fuzzy set satisfies a given linguistic expressed quantity is also investigated     

On the complexity of computing the profinite closure of a rational language

Profinite topology is used in the classification of rational languages. In particular, several important decidability problems, related to the Malcev product, reduce to the computation of the closure of a rational language in the profinite topology. It is known that, given a rational language by a deterministic automaton, computing a deterministic automaton accepting its profinite closure can be done with an exponential upper bound. This paper is dedicated the study of a lower bound for this problem: we prove that, in some cases, if the alphabet contains at least three letters, it requires an exponential time.     

Optimal secondary storage access sequence for performing relationaljoin

Two graph models are developed to determine the minimum required buffer size for achieving the theoretical lower bound on the number of disk accesses for performing relational joins. Here, the lower bound implies only one disk access per joining block or page. The first graph model is based on the block connectivity of the joining relations. Using this model, the problem of determining an ordered list of joining blocks that requires the smallest buffer is considered. It is shown that this problem as well as the problem of computing the least upper bound on the buffer size is NP-hard. The second graph model represents the page connectivity of the joining relations. It is shown that the problem of computing the least upper bound on the buffer size for the page connectivity model is also NP-hard. Heuristic procedures are presented for the page connectivity model and it is shown that the sequence obtained using the heuristics requires a near-optimal buffer size The authors also show the performance improvement of the proposed heuristics over the hybrid-has join algorithm for a wide range of join factors     

Some classes of automata as partially ordered sets

A class of automata is considered as a partially ordered set by homomorphism relation. We show first that some classes of automata. e.g., quasiperfect automata, perfect automata and strongly cofinal automata, are lattices, and other classes, e.g., strongly connected automata, cyclic automata and cofinal automata, are not lattices. At the same time, we give algorithms for computing the least upper bound and the greatest lower bound of given two elements in each class which forms a lattice.     

Reliability of a class of multistage interconnection networks

The reliability of extra-stage interconnection networks is discussed. Three types of reliability are analyzed: terminal reliability, which is the probability that at least one fault-free path exists between a given input-output pair: network reliability, which is the probability that at least one fault-free path exists between every input-output pair; and broadcast reliability, which is the probability that at least one fault-free path exists between a given input and all outputs. A recursive expression for the broadcast reliability is obtained. Tight bounds are derived for the network reliability. The numerical results indicate that for practical networks (i.e. when network reliability is at least 0.5) the difference between the upper bound and the lower bound is no more than 2% of the lower bound     

On affine state-space neural networks for system identification: Global stability conditions and complexity management

A nonlinear black box structure represented by an affine three-layered state-space neural network with exogenous inputs is considered for nonlinear systems identification. Global stability conditions are derived based on Lyapunov's stability theory and on the contraction mapping theorem. The problem of structural complexity is also addressed by defining an upper bound for the number of hidden layer neurons expressed as the cardinality of the dominant singular values of the oblique subspace projection of data driven Hankel matrices. Rank degeneracy stemming from nonlinearities, colored noise or finite data sets are dealt with either in terms of the sensitivity of singular values or by comparing the relevance of including additional coordinates in a given realization. Two examples are provided for illustrating the feasibility of derived global stability condition and the proposed approach for delaying with the complexity problem.     

On the implication problem for cardinality constraints and functional dependencies

In database design, integrity constraints are used to express database semantics. They specify the way by that the elements of a database are associated to each other. The implication problem asks whether a given set of constraints entails further constraints. In this paper, we study the finite implication problem for cardinality constraints. Our main result is a complete characterization of closed sets of cardinality constraints. Similar results are obtained for constraint sets containing cardinality constraints, but also key and functional dependencies. Moreover, we construct Armstrong databases for these constraint sets, which are of special interest for example-based deduction in database design.     

多文字可满足SAT问题的相变点上界

可满足(SAT)问题是指：是否存在一组布尔变元赋值,使得随机合取范式(CNF)公式中每个子句至少有1个文字为真。多文字可满足SAT问题是指：是否存在一组布尔变元赋值,使得随机CNF公式中每个子句至少有2个文字为真。此问题仍然是一个NP难问题。定义约束密度α为CNF公式子句数与变元数之比,对该问题的相变点上界α^*进行了研究。如果α>α^*,则多文字可满足SAT问题高概率不可满足。通过一阶矩一个简单的推断,可以证明α^*=-ln 2/ln(1-(k+1)/2^k),当k=3时,α^*=1。利用Kirousis等人的局部最大值技术,提升了多文字可满足3-SAT问题的相变点上界α^*=0.7193。最后,选择了大量数据进行实验验证,结果表明,理论结果与实验结果相吻合。