Showing papers by "French Institute for Research in Computer Science and Automation published in 1983"

Some mathematical questions related to the MHD equations

Abstract: Some questions relating to the large time behavior of the solutions of MHD equations for a viscous incompressible resistive fluid are investigated. The physical system is briefly described and the functional setting of the equations, a flow in a bounded domain or in whole space with a space periodicity property in all directions. The main existence and uniqueness results for weak and strong solutions of the MHD equations are recalled. Regularity properties and bounds on the solutions to the equations which are valid for all time are established and the concept of functional invariant sets is introduced which is contained in the space of smooth functions if the data are sufficiently regular. The squeezing property of the trajectories are stated and it is shown that any functional invariant set for the MHD equations, and in particular any attractor, has a finite Haussdorf dimension. The flow is found to be totally determined for large dimensions by a finite number of parameters. 26 references.

Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions.

Abstract: This paper concerns control of partially observable diffusions. The problem is formulated as a control problem with full information, but for the Zakai equation of nonlinear filtering. A maximum principle is derived and a treatment of the problem from the point of view of nonlinear semigroup is given.

Stochastic maximum principle for distributed parameter systems

Abstract: The paper extends the finite dimensional stochastic maximum principle to a large class of distributed parameter systems. Although this class of systems does not include all actual distributed parameter systems, the approach of this paper can be easily adapted to any particular situation.

A Combinatorial Limit to the Computing Power of VLSI Circuits

Abstract: We introduce a property of Boolean functions, called transitivity which consists of integer, polynomial, and matrix products as well as of many interesting related computational problems. We show that the area of any circuit computing a transitive function grows quadratically with the circuit's maximum data rate, expressed in bits/S. This result provides a precise analytic expression of an area-time tradeoff for a wide class of VLSI circuits. Furthermore (as shown elsewhere), this tradeoff is achievable. We have thus matching (to within a constant multiplicative factor) upper and lower complexity bounds for the three above products, in the VLSI circuits computational model.

On the performance evaluation of extendible hashing and trie searching

Abstract: A class of trees occurs both in digital searching and in schemes for maintaining dynamic hash tables. We study the distribution of height in these trees using the saddle point method of complex analysis. As a result, we derive a precise evaluation of the memory requirements of extendible hashing -- a dynamic hashing scheme -- and discuss some related implementation issues.

On the Uncapacitated Plant Location Problem. I: Valid Inequalities and Facets

Abstract: The uncapacitated plant location problem is considered as a node-packing problem. For this problem, several valid inequalities and facets are discussed. Necessary and sufficient conditions for trivial facets along with necessary conditions for nontrivial facets are derived. In addition, all of the facets for the case of three plants and three or more destinations are identified.

On the Uncapacitated Plant Location Problem. II: Facets and Lifting Theorems

Abstract: Several lifting procedures for facets of the uncapacitated plant location problem are discussed. Also, necessary and sufficient conditions for nontrivial facets with 0-1 integer coefficients are derived. In addition, all of the facets for the case of three or more plants and three destinations are identified.

Long-term average cost control problems for continuous time Markov processes: A survey

Abstract: This paper addresses the long-term average cost control of continuous time Markov processes. A survey of problems and methods contained in various works is given for continuous control, optimal stopping, and impulse control.

Supporting organizational problem solving with a work station

Abstract: Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. An approach to supporting work in the office is described. Using and extending ideas from the field of artificial intelligence (AI) we describe office work as a problem-solving activity. A knowledge-embedding language called OMEGA is used to embed knowledge of the organization into an office worker's work station in order to support the office worker in problem solving. A particular approach to reasoning about change and contradiction is discussed. This approach uses OMEGA's viewpoint mechanism, which is a general contradiction-handling facility. Unlike other knowledge representation systems, when a contradiction is reached the reasons for the contradiction can be analyzed by the deduction mechanism without having to resort to search mechanisms such as a backtracking. The viewpoint mechanism is the heart of the problem-solving support paradigm, a paradigm which supplements the classical AI view of problem solving. An example is presented in which OMEGA's facilities are used to support an office worker's problem-solving activities. The example illustrates the use of viewpoints and of OMEGA's capabilities to reason about its own reasoning processes. Categories and Subject Descriptors: H.3.4 [ Information Storage and Retrieval ]: Systems and Software— information networks ; H.4.1 [ Information Systems Applications ]: Office Automation; I.2.1 [ Artificial Intelligence ]: Applications and Expert Systems— office automation ; I.2.4 [ Artificial Intelligence ]: Knowledge Representation Formalisms and Methods— semantic networks

On some cheap control problems for diffusion processes

Abstract: On considere plusieurs cas de problemes de commande de processus de diffusion dans lesquels la fonctionnelle de cout ne depend pas explicitement de la commande. On demontre la continuite de la fonction cout optimale et on en donne une caracterisation a l'aide d'une inegalite quasivariationnelle interpretant le probleme comme la limite d'un probleme de commande impulsionnelle dont le cout tend vers zero

On deterministic control problems: An approximation procedure for the optimal cost

Abstract: In optimal control problems with continous and impulse controls, it is necessary to solve a quasi-variational inequality of Hamilton-Jacobi type. For the non-stationnary problem, we present a discretization method to solve it numerically and we show an application to the management of energy production systems.

Method and apparatus for visual telecommunications, in particular for use by the deaf

Abstract: In a system for visual telecommunications, e.g. for use by deaf people, an electronic camera (20) makes an image of a moving subject for transmission. The TV type image is passed through a contour extractor (25) to be converted to an animated cartoon line-drawing type image. The contour image is then compressed by means including a sampler (28) for image reduction, a difference detector (30) for selecting only points which change from one image to the next, a filter (34) for rejecting isolated points in the contour image, and an encoder (36) for converting sequences of on/off bits into data words for transmission, via a modem (14) over a telephone line (15). At the other end of the line a similar transmitter/receiver system decodes the received words and reconstitutes the successive images for display on a screen (46). The resulting animated cartoon type of display is adequate for communication by sign language or by lip reading, and is capable of being sufficiently compressed to be transmitted over a normal telephone line.

Resolution trajectorielle et analyse numerique des equations differentielles stochastiques

Abstract: Let (ξt) be the solution of the S.D.E. (E) of Section 1. Doss [3] has shown the existence of a difFerentiable function h and of a differentiate process parametrized by the process W,γ(W,t), such that: ξt = h(γ(W, t), Wt). For all continuous functions u, Xt is defined by: Xt = h(γ(u, t) ut). We develop a scheme of approximation of Xt (Theorems 2-6 and 3-4). This scheme has th following properties:? 1)it does not explicitly involve γ or h; this property is crucial, because,generally, h is not explicitly known, and its numerical approximation would be costly. 2)it converges to Xt, provided that u has bounded quadratic variation. 3)for u = W, it coincides with a scheme proposed by Milshtein [6] for quadratic-mean approximation. Further, we give an estimate of the error due to this scheme.

OPtimum design for potential flows

Abstract: Described in this paper is a methodology for solving a particular class of optimum design problems in Fluid Mechanics, namely optimum design problems for aerofoils when the corresponding fluid flow is potential. The methods described in this paper operate directly in the physical space, and take advantage of the variational formulation of the partial differential equation modelling the flow. The techniques of optimal control, optimization and the finite element method are used. Numerical examples are also given.

Robust non linear control of robotic manipulators

Abstract: This article addresses the problem of controlling robotic manipulators. A preliminary theoretical study is conducted so as to determine a large set of stable and robust controls for non-linear systems whose equations encompass the dynamic equations of any rigid manipulator. Sufficient conditions for obtaining a good tracking of a linear time-invariant model of reference are derived. The local stability of several well known control methods is rigourously established while it is shown that global stability requires the use of non-linear gains in the control expression. An interesting property is that the determination of such gains does not necessarily require an important knowledge of the system; which justifies the use of very simple control schemes in practice. However, a control better conditioned with respect to measurement noises is obtained when a good model of the system is used in the control derivation. Between these two alternatives lies the idea of using adjustable control gains that become large when needed and stay small otherwise. In light of this study, several control schemes proposed in the literature on the subject (including adaptive control schemes) are discussed and conclusions are drawn with a view to future studies.

Improving an algorithm for factoring polynomials over a finite field and constructing large irreducible polynomials

Abstract: Let f(x)\in {\bf F}_{q}[X] be a polynomial with simple roots to be factored. The so-called Berlekamp subalgebra B spanned over {\bf F}_{q} by the idempotents of A={\bf F}_{q}[X]/(f(X)) is considered. An exponential technique introduced earlier is based upon taking elements from B at random and enables us to obtain idempotents and, from that, the factors of f(X). This algorithm is speeded up in three ways. The concept of a separating subset of B is introduced and the McEliece operator mapping A onto B is used to construct a small separating set. {\em Factoring} subsets of {\bf F}_{q} were defined and investigated previously. The algorithm and these subsets are used together with a process introduced by F. J. McWilliams for the rapid construction of primitive idempotents. Finally, an algorithm is introduced for constructing irreducible polynomials of {\bf F}_{q}[X] of degree d , for large values of d , in which the most expensive operation is the Euclidian algorithm applied to two polynomials of degree 2d .

A theorem-prover for a decidable subset of default logic

Abstract: Non-monotonic logic is an attempt to take into account such notions as incomplete knowledge and theory evolution. However the decidable theorem-prover issue has been so far unexplored. We propose such a theorem-prover for default logic with a restriction on the first-order formulae it deals with. This theorem-prover is based on the generalisation of a resolution technique named saturation, which was initially designed to test the consistency of a set of first-order formulae. We have proved that our algorithm is complete and that it always terminates for the selected subset of first-order formulae.

Relational queries in a domain based DBMS

Abstract: This paper addresses the problem of relational queries processing in the domain based database machine DBMAC A brief description of the storage organisation of the domain based DBMS is first given Then the operating principles of the domain based data-model, called D-model, is described through some examples The central part of the paper deals with the translation of relational queries into operations on objects of the D-model Objects of the D-model and a set of operations on these objects are first defined : this set S of operations is shown to be complete in that any relational query can be translated into D-model operations belonging to SFinally we give a method for processing relation queries using D-model operationsThe basic advantages to be expected from a domain based physical organization of data are :1 fast equi-join execution,2 a compact representation of intermediate resultsThe latter should lead to efficient processing of complex queries, provided a powerful parallel physical architecture is chosen for implementation

Towards a Flexible Vision System

Abstract: A Vision System designed for building accurate models of industrial parts is described. Potential applications include tolerancing testing, data base acquisition and automatic recognition of objects. The system is made of a laser rangefinder that measures the position in space of points on the parts by active stereoscopy, a table on which the parts are positioned and can be translated vertically and rotated under computer control, and a set of algorithms to produce accurate geometric models of the part based on the measurements made by the laser. Representation and recognition results are presented on a variety of objects as shaded graphics displays.

Some remarks on the construction of higher order algorithms in convex optimization

Abstract: Consider the problem of minimizing a real functionalf. A Newton-like method requires first an approximationD(d) off(x + d)−f(x) at the current iteratex, valid for smalld to an order higher than 1, and consists in minimizingD. In this paper, we will introduce a new concept of such an approximation for convex functions without differentiability assumptions. The connections with the classical concept based on the Taylor development of a differentiablef are exhibited. The material is used to study a conceptual (nonimplementable) algorithm. Some hints are given which could lead to an implementable version.

Complete Sets of Unifiers and Matchers in Equational Theories

Abstract: We propose an abstract framework to present unification and matching problems. We argue about the necessity of a somewhat complicated definition of basis of unifiers (resp. matchers). In particular we prove the non-existence of complete sets of minimal unifiers (resp. matchers) in some equational theories, even regular.

Steady-State Probabilities for a Queue with a General Service Distribution and State-Dependent Arrivals

Abstract: We consider a queueing system with a general service distribution having a possibility of feedback. The customers belong to the same class, and the queueing discipline is first-in, first-out. There is only one server in the station. The facility is rendered Markovian by means of fictitious stages. The input flow depends on the state of the station. It is shown that the equilibrium probabilities can be simply expressed by means of a matrix product. Two particular cases are studied.

Prism trees: a hierarchical representation for 3-D objects

Abstract: In this paper we propose a new hierarchical structure for describing 5-0 objects, called the Prism Tree. This ternar tree structure, inspired from the planar Strip Tree, is built from an initial trianguiation of the object by using a polyhedral approximation algorithm. Different properties of this representation are shown, as well as algorithms for intersecting objects and neighbor finding techniques.