We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and or termination modulo E. In contrast, our method is based solely on usual critical pairs and usual termination. We first present confluence criteria for term rewriting systems whose rewrite rules can be partitioned into terminating part and possibly non-terminating part. We then give a reduction-preserving completion procedure so that the applicability of the criteria is enhanced. In contrast to the well-known Knuth-Bendix completion procedure which preserves the equivalence relation of the system, our completion procedure preserves the reduction relation of the system, by which confluence of the original system is inferred from that of the completed system.
The decreasing diagram technique @cite_0 is a powerful technique to obtain many confluence criteria. In @cite_20 , the technique is extended to obtain a criterion for CRM.
@cite_0 @cite_20
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The decreasing diagrams technique is a complete method to reduce confluence of a rewrite relation to local confluence. Whereas previous presentations have focussed on the proofthe technique is correct, here we focus on applicability. We present a simple but powerful generalisation of the technique, requiring peaks to be closed only by conversions instead of valleys, which is demonstrated to further ease applicability. The persistence diagram of a filtered simplicial complex is usually computed by reducing the boundary matrix of the complex. We introduce a simple optimization technique: by processing the simplices of the complex in decreasing dimension, we can “kill” columns (i.e., set them to zero) without reducing them. This technique completely avoids reduction on roughly half of the columns. We demonstrate that this idea significantly improves the running time of the reduction algorithm in practice. We also give an output-sensitive complexity analysis for the new algorithm which yields to sub-cubic asymptotic bounds under certain assumptions. We study communication networks that employ drop-tail queueing and Additive-Increase Multiplicative-Decrease (AIMD) congestion control algorithms. It is shown that the theory of nonnegative matrices may be employed to model such networks. In particular, important network properties, such as: 1) fairness; 2) rate of convergence; and 3) throughput, can be characterized by certain nonnegative matrices. We demonstrate that these results can be used to develop tools for analyzing the behavior of AIMD communication networks. The accuracy of the models is demonstrated by several NS studies. This papers analyzes a class of nonlinear additive-increase multiplicative-decrease (AIMD) protocols that are widely deployed in communication networks. It is demonstrated that the use of these protocols guarantees that the system has a unique stable outcome to which it converges geometrically under all starting points. The development is based on a contraction argument and the derivation of explicit bounds on the contraction coefficient of corresponding operators in terms of the network parameters. In particular, bounds on the corresponding rate of convergence are obtained, improving upon known bounds for standard (linear) AIMD networks. We address the problem of graph rewriting and narrowing as the underlying operational semantics of rule-based programming languages. We propose new optimal graph rewriting and narrowing strategies in the setting of orthogonal constructor-based graph rewriting systems. For this purpose, we first characterize a subset of graphs, called admissible graphs. A graph is admissible if none of its defined operations belongs to a cycle. We then prove the confluence, as well as the confluence modulo bisimilarity (unraveling), of the admissible graph rewriting relation. Afterwards, we define a sequential graph rewriting strategy by using Antoy’s definitional trees. We show that the resulting strategy computes only needed redexes and develops optimal derivations w.r.t. the number of steps. Finally, we tackle the graph narrowing relation over admissible graphs and propose a sequential narrowing strategy which computes independent solutions and develops shorter derivations than most general graph narrowing. Tabu search techniques are used for moving step by step towards the minimum value of a function. A tabu list of forbidden movements is updated during the iterations to avoid cycling and being trapped in local minima. Such techniques are adapted to graph coloring problems. We show that they provide almost optimal colorings of graphs having up to 1000 nodes and their efficiency is shown to be significantly superior to the famous simulated annealing. In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of a filtered simplicial complex. For any @C>0, it returns only those homology classes with persistence at least @C. Instead of the classical reduction via column operations, our algorithm performs rank computations on submatrices of the boundary matrix. For an arbitrary constant @[email protected]?(0,1), the running time is O(C"("1"-"@d")"@CR"d(n)logn), where C"("1"-"@d")"@C is the number of homology classes with persistence at least ([email protected])@C, n is the total number of simplices in the complex, d its dimension, and R"d(n) is the complexity of computing the rank of an nxn matrix with O(dn) nonzero entries. Depending on the choice of the rank algorithm, this yields a deterministic O(C"("1"-"@d")"@Cn^2^.^3^7^6) algorithm, an O(C"("1"-"@d")"@Cn^2^.^2^8) Las-Vegas algorithm, or an O(C"("1"-"@d")"@Cn^2^+^@e) Monte-Carlo algorithm for an arbitrary @e>0. The space complexity of the Monte-Carlo version is bounded by O(dn)=O(nlogn). This paper presents a relational framework for studying properties of labeled data points related to proximity and labeling information in order to improve the performance of the 1NN rule. Specifically, the class conditional nearest neighbor (ccnn) relation over pairs of points in a labeled training set is introduced. For a given class label c, this relation associates to each point a its nearest neighbor computed among only those points with class label c (excluded a). A characterization of ccnn in terms of two graphs is given. These graphs are used for defining a novel scoring function over instances by means of an information-theoretic divergence measure applied to the degree distributions of these graphs. The scoring function is employed to develop an effective large margin instance selection method, which is empirically demonstrated to improve storage and accuracy performance of the 1NN rule on artificial and real-life data sets. While numerous metrics for information retrieval are available in the case of binary relevance, there is only one commonly used metric for graded relevance, namely the Discounted Cumulative Gain (DCG). A drawback of DCG is its additive nature and the underlying independence assumption: a document in a given position has always the same gain and discount independently of the documents shown above it. Inspired by the "cascade" user model, we present a new editorial metric for graded relevance which overcomes this difficulty and implicitly discounts documents which are shown below very relevant documents. More precisely, this new metric is defined as the expected reciprocal length of time that the user will take to find a relevant document. This can be seen as an extension of the classical reciprocal rank to the graded relevance case and we call this metric Expected Reciprocal Rank (ERR). We conduct an extensive evaluation on the query logs of a commercial search engine and show that ERR correlates better with clicks metrics than other editorial metrics. We give a O(slog n)-approximation algorithm for the sparsest cut, edge expansion, balanced separator, and graph conductance problems. This improves the O(log n)-approximation of Leighton and Rao (1988). We use a well-known semidefinite relaxation with triangle inequality constraints. Central to our analysis is a geometric theorem about projections of point sets in Rd, whose proof makes essential use of a phenomenon called measure concentration. We also describe an interesting and natural “approximate certificate” for a graph's expansion, which involves embedding an n-node expander in it with appropriate dilation and congestion. We call this an expander flow. Restoration of writing order from a single-stroked handwriting image can be seen as the problem of finding the smoothest path in its graph representation. In this paper, a 3-phase approach to restore a writing order is proposed within the framework of the edge continuity relation (ECR). In the initial, local phase, in order to obtain possible ECRs at an even-degree node, a neural network is used for the node of degree 4 and a theoretical approach is presented for the node of degree higher than 4 by introducing certain reasonable assumptions. In the second phase, we identify double-traced lines by employing maximum weighted matching. This makes it possible to transform the problem of obtaining possible ECRs at odd-degree node to that at even-degree node. In the final, global phase, we find all the candidates of single-stroked paths by depth first search and select the best one by evaluating SLALOM smoothness. Experiments on static images converted from online data in the Unipen database show that our method achieves a restoration rate of 96.0 percent Linear support vector machines (SVM) are useful for classifying large-scale sparse data. Problems with sparse features are common in applications such as document classification and natural language processing. In this paper, we propose a novel coordinate descent algorithm for training linear SVM with the L2-loss function. At each step, the proposed method minimizes a one-variable sub-problem while fixing other variables. The sub-problem is solved by Newton steps with the line search technique. The procedure globally converges at the linear rate. As each sub-problem involves only values of a corresponding feature, the proposed approach is suitable when accessing a feature is more convenient than accessing an instance. Experiments show that our method is more efficient and stable than state of the art methods such as Pegasos and TRON. Bounded increase is a termination technique where it is tried to find an argument x of a recursive function that is increased repeatedly until it reaches a bound b, which might be ensured by a condition x<b. Since the predicates like < may be arbitrary user-defined recursive functions, an induction calculus is utilized to prove conditional constraints. In this paper, we present a full formalization of bounded increase in the theorem prover Isabelle HOL. It fills one large gap in the pen-and-paper proof, and it includes generalized inference rules for the induction calculus as well as variants of the Babylonian algorithm to compute square roots. These algorithms were required to write executable functions which can certify untrusted termination proofs from termination tools that make use of bounded increase. And indeed, the resulting certifier was already useful: it detected an implementation error that remained undetected since 2007. This paper reports on a novel technique for literature indexing and searching in a mechanized library system. The notion of relevance is taken as the key concept in the theory of information retrieval and a comparative concept of relevance is explicated in terms of the theory of probability. The resulting technique called “Probabilistic Indexing,” allows a computing machine, given a request for information, to make a statistical inference and derive a number (called the “relevance number”) for each document, which is a measure of the probability that the document will satisfy the given request. The result of a search is an ordered list of those documents which satisfy the request ranked according to their probable relevance. The paper goes on to show that whereas in a conventional library system the cross-referencing (“see” and “see also”) is based solely on the “semantical closeness” between index terms, statistical measures of closeness between index terms can be defined and computed. Thus, given an arbitrary request consisting of one (or many) index term(s), a machine can elaborate on it to increase the probability of selecting relevant documents that would not otherwise have been selected. Finally, the paper suggests an interpretation of the whole library problem as one where the request is considered as a clue on the basis of which the library system makes a concatenated statistical inference in order to provide as an output an ordered list of those documents which most probably satisfy the information needs of the user. The Web offers rich relational data with different semantics. In this paper, we address the problem of document recommendation in a digital library, where the documents in question are networked by citations and are associated with other entities by various relations. Due to the sparsity of a single graph and noise in graph construction, we propose a new method for combining multiple graphs to measure document similarities, where different factorization strategies are used based on the nature of different graphs. In particular, the new method seeks a single low-dimensional embedding of documents that captures their relative similarities in a latent space. Based on the obtained embedding, a new recommendation framework is developed using semi-supervised learning on graphs. In addition, we address the scalability issue and propose an incremental algorithm. The new incremental method significantly improves the efficiency by calculating the embedding for new incoming documents only. The new batch and incremental methods are evaluated on two real world datasets prepared from CiteSeer. Experiments demonstrate significant quality improvement for our batch method and significant efficiency improvement with tolerable quality loss for our incremental method. Geometric heuristics for the quantifier elimination approach presented by Kapur (2004) are investigated to automatically derive loop invariants expressing weakly relational numerical properties (such as l≤x≤h or l≤±x ±y≤h) for imperative programs. Such properties have been successfully used to analyze commercial software consisting of hundreds of thousands of lines of code (using for example, the Astree tool based on abstract interpretation framework proposed by Cousot and his group). The main attraction of the proposed approach is its much lower complexity in contrast to the abstract interpretation approach (O(n2) in contrast to O(n4), where n is the number of variables) with the ability to still generate invariants of comparable strength. This approach has been generalized to consider disjunctive invariants of the similar form, expressed using maximum function (such as max (x+a,y+b,z+c,d)≤max (x+e,y+f,z+g,h)), thus enabling automatic generation of a subclass of disjunctive invariants for imperative programs as well. Despite the importance of data mining techniques to customer relationship management (CRM), there is a lack of a comprehensive literature review and a classification scheme for it. This is the first identifiable academic literature review of the application of data mining techniques to CRM. It provides an academic database of literature between the period of 2000-2006 covering 24 journals and proposes a classification scheme to classify the articles. Nine hundred articles were identified and reviewed for their direct relevance to applying data mining techniques to CRM. Eighty-seven articles were subsequently selected, reviewed and classified. Each of the 87 selected papers was categorized on four CRM dimensions (Customer Identification, Customer Attraction, Customer Retention and Customer Development) and seven data mining functions (Association, Classification, Clustering, Forecasting, Regression, Sequence Discovery and Visualization). Papers were further classified into nine sub-categories of CRM elements under different data mining techniques based on the major focus of each paper. The review and classification process was independently verified. Findings of this paper indicate that the research area of customer retention received most research attention. Of these, most are related to one-to-one marketing and loyalty programs respectively. On the other hand, classification and association models are the two commonly used models for data mining in CRM. Our analysis provides a roadmap to guide future research and facilitate knowledge accumulation and creation concerning the application of data mining techniques in CRM. Abstract We present in this paper a unified processing for real, integer, and Boolean constraints based on a general narrowing algorithm which applies to any n-ary relation on R. The basic idea is to define, for every such relation ρ, a narrowing function ρ based on the approximation of ρ by a Cartesian product of intervals whose bounds are floating-point numbers. We then focus on nonconvex relations and establish several properties. The more important of these properties is applied to justify the computation of usual relations defined in terms of intersections of simpler relations. We extend the scope of the narrowing algorithm used in the language BNR-Prolog to integer and disequality constraints, to Boolean constraints, and to relations mixing numerical and Boolean values. As a result, we propose a new Constraint Logic Programming language called CLP(BNR), where BNR stands for Booleans, Naturals, and Reals. In this language, constraints are expressed in a unique structure, allowing the mixing of real numbers, integers, and Booleans. We end with the presentation of several examples showing the advantages of such an approach from the point of view of the expressiveness, and give some preliminary computational results from a prototype. The Frank and Wolfe method of feasible directions is shown to be a case of the more general computational approach of inner linearization followed by restriction. An extension is proposed based on this observation. The extended procedure converges, and under certain conditions the asymptotic convergence rate is geometric. Limited computational experience comparing the two procedures is reported. The innovation of this work is a simple vectorizable algorithm for performing sparse matrix vector multiply in compressed sparse row (CSR) storage format. Unlike the vectorizable jagged diagonal format (JAD), this algorithm requires no data rearrangement and can be easily adapted to a sophisticated library framework such as PETSc. Numerical experiments on the Cray X1 show an order of magnitude improvement over the non-vectorized algorithm.