(Incremental) Priority Algorithms

We study the question of which optimization problems can be optimally or approximately solved by greedy or greedy-like algorithms. For definiteness, we limit the present discussion to some well-studied scheduling problems although the underlying issues apply in a much more general setting. Of course, the main benefit of greedy algorithms lies in both their conceptual simplicity and their computational efficiency. Based on the experience from online competitive analysis, it seems plausible that we should be able to derive approximation bounds for greedy-like algorithms exploiting only the conceptual simplicity of these algorithms. To this end, we need (and will provide) a precise definition of what we mean by greedy and greedy-like.     

Sur les générateurs algébriques et linéaires

Résumé Nous étudions certaines propriétés des générateurs algébriques et linéaires. Nous montrons que le langage algébrique E engendré par la grammaire: S aSbSc + d domine tous les langages algébriques par applications séquentielles fidèles. Nous en déduisons que pour tout langage algébrique L et tout générateur algébrique L, il existe une transduction rationnelle fonctionnelle et fidèle telle que L=(L). Ce résultat, qui n'est pas vérifié pour la famille, Lin, des langages algébriques linéaires, nous permet de montrer qu'aucun générateur algébrique n'appartient à la famille EDTOL. Enfin, nous établissons que si L est un générateur linéaire, L # est un générateur séquentiel pour Lin.

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Algebraic and linear generators

Summary We study some properties of algebraic and linear generators. We show that the algebraic language E generated by the grammar: S aSbSc + d dominates every algebraic language by faithful sequential mappings. We deduce that, for every algebraic language L and every algebraic generator L, there exists a faithful rational function such that L=(L). This result, which does not hold for the family of linear languages, permits us to show that no algebraic generator belongs to the family EDTOL. Also, we prove if L is a linear generator then L # is a sequential generator for Lin.

     

Utilizing deontic operators in information systems specification

One major task in requirements specification is to capture the rules relevant to the problem at hand. Declarative, rule-based approaches have been suggested by many researchers in the field. However, when it comes to modeling large systems of rules, not only for the behavior of the computer system but also for the organizational environment surrounding it, current approaches have problems with limited expressiveness, flexibility, and poor comprehensibility. Hence, rule-based approaches may benefit from improvements in two directions: (1) improvement of the rule languages themselves and (2) better integration with other, complementary modeling approaches.In this article, both issues are addressed in an integrated manner. The proposal is presented in the context of the Tempora project on rule-based information systems development, but has also been integrated with PPP. Tempora has provided a rule language based on an executable temporal logic working on top of a temporal database. The rule language is integrated with static (ER-like) and dynamic (SA/RT-like) modeling approaches. In the current proposal, the integration with complementary modeling approaches is extended by including organization modeling (actors, roles), and the expressiveness of the rule language is increased by introducing deontic operators and rule hierarchies. The main contribution of the article is not seen as any one of the above-mentioned extensions, but as the resulting comprehensive modeling support. The approach is illustrated by examples taken from an industrial case study done in connection with Tempora.C. List of Symbols Subset of set - Not subset of set - Element of set - Not element of set - Equivalent to - Not equivalent to - ¬ Negation - Logical and - Logical or - Implication - Sometime in past - Sometime in future - Always in past - Always in future - Just before - Just after - u Until - s Since - Trigger - Condition - _s State condition - Consequence - _a Action - _s State - Role - Actor - ¬ - General deontic operator - O Obligatory - R Recommended - P Permitted - D Discouraged - F Forbidden - (/–) General rule - t _R Real time - t _M Model time     

Bicentres de langages algébriques

Resume Les notions de bicentre et bicentre strict d'un langage, définies par A. De Luca, A. Restivo et S. Salemi généralisent la notion de centre d'un langage définie par M. Nivat. L'objet du présent papier est de répondre á la question suivante lorsque désigne la famille des langages algébriques ou l'une de ses sous-familles classiques:Si L appartient à , le bicentre de L (respectivement le bicentre strict de L) appartient-il à ?Le principal résultat est une réponse positive à cette question lorsqu'il s'agit de la notion de bicentre et que est un full-AFL uniforme de langages algébriques.

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Bicenters of context-free languages

Summary The notions of bicenter and strict bicenter of a language have been defined by A. De Luca, A. Restivo and S. Salemi and are a generalisation of the notion of center of a language, defined by M, Nivat. This paper deals with the following question, when is the family of context-free languages or one of its classical subfamilies:when L is in , is the bicenter (resp. the strict bicenter) of L also in ?Concerning the notion of bicenter, the main result of the paper is a positive answer when is a uniform full-AFL of context-free languages.

     

On Topological Watersheds

In this paper, we investigate topological watersheds (Couprie and Bertrand, 1997). One of our main results is a necessary and sufficient condition for a map G to be a watershed of a map F, this condition is based on a notion of extension. A consequence of the theorem is that there exists a (greedy) polynomial time algorithm to decide whether a map G is a watershed of a map F or not. We introduce a notion of separation between two points of an image which leads to a second necessary and sufficient condition. We also show that, given an arbitrary total order on the minima of a map, it is possible to define a notion of degree of separation of a minimum relative to this order. This leads to a third necessary and sufficient condition for a map G to be a watershed of a map F. At last we derive, from our framework, a new definition for the dynamics of a minimum.Gilles Bertrand received his Ingénieurs degree from the École Centrale des Arts et Manufactures in 1976. Until 1983 he was with the Thomson-CSF company, where he designed image processing systems for aeronautical applications. He received his Ph.D. from the École Centrale in 1986. He is currently teaching and doing research with the Laboratoire Algorithmique et Architecture des Systémes Informatiques, ESIEE, Paris, and with the Institut Gaspard Monge, Université de Marne-la-Vallée. His research interests are image analysis, discrete topology and mathematical morphology.     

What holds in a context?

In order to establish that [A] = [B] follows from a set of assumptions often one provesA =B and then invokes the principle of substitution of equals for equals. It has been observed that in the ancillary proof ofA =B one is allowed to use, in addition to those assumptions of which are free for , certain (open) sentencesP which may not be part of and may not follow from , but are related to the context . We show that in an appropriate formal system there is a closed form solution to the problem of determining precisely what sentencesP can be used. We say that those sentenceshold in the context under the set of assumptions . We suggest how the solution could be exploited in an interactive theorem prover.     

Specification and verification of database dynamics

Summary A framework is proposed for the structured specification and verification of database dynamics. In this framework, the conceptual model of a database is a many sorted first order linear tense theory whose proper axioms specify the update and the triggering behaviour of the database. The use of conceptual modelling approaches for structuring such a theory is analysed. Semantic primitives based on the notions of event and process are adopted for modelling the dynamic aspects. Events are used to model both atomic database operations and communication actions (input/output). Nonatomic operations to be performed on the database (transactions) are modelled by processes in terms of trigger/reaction patterns of behaviour. The correctness of the specification is verified by proving that the desired requirements on the evolution of the database are theorems of the conceptual model. Besides the traditional data integrity constraints, requirements of the form Under condition W, it is guaranteed that the database operation Z will be successfully performed are also considered. Such liveness requirements have been ignored in the database literature, although they are essential to a complete definition of the database dynamics.

Notation

Classical Logic Symbols (Appendix 1) for all (universal quantifier) - exists at least once (existential quantifier) - ¬ no (negation) - implies (implication) - is equivalent to (equivalence) - and (conjunction) - or (disjunction) Tense Logic Symbols (Appendix 1) G always in the future - G ₀ always in the future and now - F sometime in the future - F ₀ sometime in the future or now - H always in the past - H ₀ always in the past and now - P sometime in the past - P ₀ sometime in the past or now - X in the next moment - Y in the previous moment - L always - M sometime Event Specification Symbols (Sects. 3 and 4.1) (x) means immediately after the occurrence of x - (x) means immediately before the occurrence of x - (x) means x is enabled, i.e., x may occur next - { } ({w ₁} x{w ₂}) states that if w ₁ holds before the occurrence of x, then w ₂ will hold after the occurrence of x (change rule) - [ ] ([oa₁, ..., oa_n]x) states that only the object attributes oa₁, ..., oa _n are modifiable by x (scope rule) - {{ }} ({{w}}x) states that if x may occur next, then w holds (enabling rule) Process Specification Symbols (Sects. 5.3 and 5.4) :: for causal rules - for behavioural rules Transition-Pattern Composition Symbols (Sects. 5.2 and 5.3) ; sequential composition - ¦ choice composition - parallel composition - :| guarded alternative composition Location Predicates (Sect. 5.2) (z) means immediately after the occurrence of the last event of z (after) - (z) means immediately before the occurrence of the first event of z (before) - (z) means after the beginning of z and before the end of z (during) - ( z) means before the occurrence of an event of z (at)     

Parallel construction of a suffix tree with applications

Many string manipulations can be performed efficiently on suffix trees. In this paper a CRCW parallel RAM algorithm is presented that constructs the suffix tree associated with a string ofn symbols inO(logn) time withn processors. The algorithm requires (n ²) space. However, the space needed can be reduced toO(n ¹⁺) for any 0< 1, with a corresponding slow-down proportional to 1/. Efficient parallel procedures are also given for some string problems that can be solved with suffix trees.The results of this paper have been achieved independently and simultaneously in [AI-86] and [LSV-86]. The research of U. Vishkin was supported by NSF Grant NSF-CCR-8615337, ONR Grant N00014-85-K-0046, and Foundation for Research in Electronics, Computers, and Communication, administered by the Israeli Academy of Sciences and Humanities. The research of A. Apostolico was carried out in part while visiting at the Istituto di Analisi dei Sistemi e Informatica, Rome, with support from the Italian National Research Council. The research of G. M. Landau, B. Schieber, and U. Vishkin was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy under Contract DE-AC02-76ER03077.     

Long unavoidable patterns

Summary We examine long unavoidable patterns, unavoidable in the sense of Bean, Ehrenfeucht, McNulty. Zimin and independently Schmidt have shown that there is only one unavoidable pattern of length 2 ⁿ -1 on an alphabet with n letters; this pattern is a quasi-power in the sense of Schützenberger. We characterize the unavoidable words of length 2 ⁿ -2 and 2 ⁿ -3. Finally we show that every sufficiently long unavoidable word has a certain quasi-power as a subword.This work was done while the author stayed at LITP, Université Paris 6, France     

Parallel complexity of logical query programs

We consider the parallel time complexity of logic programs without function symbols, called logical query programs, or Datalog programs. We give a PRAM algorithm for computing the minimum model of a logical query program, and show that for programs with the polynomial fringe property, this algorithm runs in time that is logarithmic in the input size, assuming that concurrent writes are allowed if they are consistent. As a result, the linear and piecewise linear classes of logic programs are inN C. Then we examine several nonlinear classes in which the program has a single recursive rule that is an elementary chain. We show that certain nonlinear programs are related to GSM mappings of a balanced parentheses language, and that this relationship implies the polynomial fringe property; hence such programs are inN C Finally, we describe an approach for demonstrating that certain logical query programs are log space complete forP, and apply it to both elementary single rule programs and nonelementary programs.Supported by NSF Grant IST-84-12791, a grant of IBM Corporation, and ONR contract N00014-85-C-0731.     

Unitary immersions of nonlinear systems

In this paper, we define what we call a unitary immersion of a nonlinear system. We observe that, for classical Hamiltonian systems, this notion contains, in some sense, the concept of quantization. We restrict our attention to degree-zero unitary immersions, where all observation functions must be represented by operators of the type multiplication by a function. We show that the problem of classifying such degree-zero unitary immersions of a given nonlinear system is not obvious. In some cases, we solve this problem.Chargé de Recherche au CNRS.Maître de Conférences.     

A Hyperbase for Binary Lattice Hyperidentities

We define an identity to be hypersatisfied by a variety V if, whenever the operation symbols of V, are replaced by arbitrary terms (of appropriate arity) in the operations of V, the resulting identity is satisfied by V in the usual sense. Whenever the identity is hypersatisfied by a variety V, we shall say that is a V hyperidentity. For example, the identity x + x y = x (x + y) is hypersatisfied by the variety L of all lattices. A proof of this consists of a case-by-case examination of { + , } {x, y, x y, x y}, the set of all binary lattice terms. In an earlier work, we exhibited a hyperbase ^L for the set of all binary lattice (or, equivalently, quasilattice) hyperidentities of type 2, 2. In this paper we provide a greatly refined hyperbase _L . The proof that _L is a hyperbase was obtained by using the automated reasoning program Otter 3.0.4.     

Generating Boolean \mu-expressions

In this paper, we consider the class of Boolean -functions, which are the Boolean functions definable by -expressions (Boolean expressions in which no variable occurs more than once). We present an algorithm which transforms a Boolean formulaE into an equivalent -expression-if possible-in time linear in E times , where E is the size ofE andn _m is the number of variables that occur more than once inE. As an application, we obtain a polynomial time algorithm for Mundici's problem of recognizing -functions fromk-formulas [17]. Furthermore, we show that recognizing Boolean -functions is co-NP-complete for functions essentially dependent on all variables and we give a bound close to co-NP for the general case.     

A two-layer fuzzy pattern matching procedure for the evaluation of conditions involving vague quantifiers

In this note, we are interested in the evaluation of conditions of the form The value of attribute a for Q items of X is in F or more shortly Q items of X are F, where X is a set of items, Q denotes a possibly vague proportion (which may be linguistically expressed, e.g. most), F is a (possibly fuzzy) subset of the attribute domain of a. and where the available knowledge about the value a(x) of the attribute a for any item x may be imprecise or even vague. The evaluation is based on a fuzzy pattern matching procedure repeated two times. Such conditions may be encountered in queries addressed to an incomplete information data base or in the if-part of expert rules.     

Probabilistic analysis of the application of the cross ratio to model based vision: Misclassification

The cross ratio of four colinear points is of fundamental importance in model based vision, because it is the simplest numerical property of an object that is invariant under projection to an image. It provides a basis for algorithms to recognise objects from images without first estimating the position and orientation of the camera.A quantitative analysis of the effectiveness of the cross ratio in model based vision is made. A given imageI of four colinear points is classified by making comparisons between the measured cross ratio of the four image points and the cross ratios stored in the model database. The imageI is accepted as a projection of an objectO with cross ratio if |–|ntu, wheren is the standard deviation of the image noise,t is a threshold andu=. The performance of the cross ratio is described quantitatively by the probability of rejectionR, the probability of false alarmF and the probability of misclassificationp (), defined for two model cross ratios , . The trade off between these different probabilities is determined byt.It is assumed that in the absence of an object the image points have identical Gaussian distributions, and that in the presence of an object the image points have the appropriate conditional densities. The measurements of the image points are subject to small random Gaussian perturbations. Under these assumptions the trade offs betweenR,F andp () are given to a good approximation byR=2(1–(t)),F=r _F t, t|–|^–1, where is the relative noise level, is cumulative distribution function for the normal distribution,r _F is constant, ande is a function of only. The trade off betweenR andF is obtained in Maybank (1994). In this paper the trade off betweenR andp () is obtained.It is conjectured that the general form of the above trade offs betweenR,F andp () is the same for a range of invariants useful in model based vision. The conjecture prompts the following definition: an invariant which has trade offs betweenR,F,p () of the above form is said to benon-degenerate for model based vision.The consequences of the trade off betweenR andp () are examined. In particular, it is shown that for a fixed overall probability of misclassification there is a maximum possible model cross ratio _m , and there is a maximum possible numberN of models. Approximate expressions for _m andN are obtained. They indicate that in practice a model database containing only cross ratio values can have a size of order at most ten, for a physically plausible level of image noise, and for a probability of misclassification of the order 0.1.     

On Test Data Compression Using Selective Don t-Care Identification

This paper proposes an effective method for reducing test data volume under multiple scan chain designs. The proposed method is based on reduction of distinct scan vectors using selective don‘t-care identification. Selective don‘t-care identification is repeatedly executed under condition that each bit of frequent scan vectors is fixed to binary values (0 or1). Besides, a code extension technique is adopted for improving compression efficiency with keeping decompressor circuits simple in the manner that the code length for infrequent scan vectors is designed as double of that for frequent ones. The effectiveness of the proposed method is shown through experiments for ISCAS‘89 and ITC‘99 benchmark circuits.     

On Bounding Solutions of Underdetermined Systems

Sufficient conditions for the existence and uniqueness of a solution x* D (R ⁿ ) of Y(x) = 0 where : R ⁿ R ^m (m n) with C ²(D) where D R ⁿ is an open convex set and Y = (x)⁺ are given, and are compared with similar results due to Zhang, Li and Shen (Reliable Computing 5(1) (1999)). An algorithm for bounding zeros of f (·) is described, and numerical results for several examples are given.     

From Conditional Events to Conditional Measures: A New Axiomatic Approach

Our starting point is a definition of conditional event EH which differs from many seemingly similar ones adopted in the relevant literature since 1935, starting with de Finetti. In fact, if we do not assign the same third value u (undetermined) to all conditional events, but make it depend on EH, it turns out that this function t(EH) can be taken as a general conditional uncertainty measure, and we get (through a suitable – in a sense, compulsory – choice of the relevant operations among conditional events) the natural axioms for many different (besides probability) conditional measures.     

Quasi-Linear Algorithms for the Topological Watershed

The watershed transformation is an efficient tool for segmenting grayscale images. An original approach to the watershed (Bertrand, Journal of Mathematical Imaging and Vision, Vol. 22, Nos. 2/3, pp. 217–230, 2005.; Couprie and Bertrand, Proc. SPIE Vision Geometry VI, Vol. 3168, pp. 136–146, 1997.) consists in modifying the original image by lowering some points while preserving some topological properties, namely, the connectivity of each lower cross-section. Such a transformation (and its result) is called a W-thinning, a topological watershed being an ultimate W-thinning. In this paper, we study algorithms to compute topological watersheds. We propose and prove a characterization of the points that can be lowered during a W-thinning, which may be checked locally and efficiently implemented thanks to a data structure called component tree. We introduce the notion of M-watershed of an image F, which is a W-thinning of F in which the minima cannot be extended anymore without changing the connectivity of the lower cross-sections. The set of points in an M-watershed of F which do not belong to any regional minimum corresponds to a binary watershed of F. We propose quasi-linear algorithms for computing M-watersheds and topological watersheds. These algorithms are proved to give correct results with respect to the definitions, and their time complexity is analyzed.Michel Couprie received his Ingénieurs degree from the École Supérieure dIngénieurs en Électrotechnique et Électronique (Paris, France) in 1985 and the Ph.D. degree from the Pierre et Marie Curie University (Paris, France) in 1988. Since 1988 he has been working in ESIEE where he is an Associate Professor. He is a member of the Laboratoire Algorithmique et Architecture des Systémes Informatiques, ESIEE, Paris, and of the Institut Gaspard Monge, Universit é de Marne-la-Vallée. His current research interests include image analysis and discrete mathematics.Laurent Najman received his Ph.D. of applied mathematics from Paris-Dauphine university and an Ingénieurs degree from the Ecole des Mines de Paris. After earning his Ingénieurs degree, he worked in the research laboratories of Thomson-CSF for three years, before joining Animation Science in 1995, as director of research and development. In 1998, he joined OcÉ Print Logic Technolgies, as senior scientist. Since 2002, he is associate professor with the A2SI laboratory of ESIEE, Paris. His current research interest is discrete mathematical morphology.Gilles Bertrand received his Ingénieurs degree from the École Centrale des Arts et Manufactures in 1976. Until 1983 he was with the Thomson-CSF company, where he designed image processing systems for aeronautical applications. He received his Ph. from the École Centrale in 1986. He is currently teaching and doing research with the Laboratoire Algorithmique et Architecture des Systémes Informatiques, ESIEE, Paris, and with the Institut Gaspard Monge, Université de Marne-la-Vallée. His research interests are image analysis, pattern recognition, mathematical morphology and digital topology.     

Mapping dynamic programming onto modular linear systolic arrays

Summary In this paper we propose a novel way of deriving a family of fully-pipelined linear systolic algorithms for the computation of the solutions of a dynamic programming problem. In many instances, modularity is an important feature of these algorithms. One may simply add more processors to the array as the size of the problem increases. Each cell has a fixed amount of local storage and the time delay between two consecutive cells of the array is constant. The time complexity and the number of cells in our array tend ton ²+O(n) andn ²/ +O(n), respectively, as increases. This represents the best known performance for such an algorithm. Jean Frédéric Myoupo received his B.Sc in mathematics from the University of Yaounde, Cameroon, in 1980, and the M.S. and Ph.D. degrees both in applied mathematics from the Université Paul Sabatier de Toulouse, France in 1981 and 1983 respectively. From 1983 to 1985, he was lecturer at the Université de Sherbrooke, Québec, Canada. From 1985 to 1990, he was Assistant-Professor at the University of Yaounde, Cameroon. Since October 1990, he has been Associate-Professor in the department d'Informatique and Laboratoire de Recherche en Informatique (L.R.I.) of the Université de Paris-Sud, France. His current research interests include design of systolic algorithms and architectures, parallel and distributed processing.