Abstract: In a system, utilized in, e.g., scheduling, for satisfying constraints by allowing relaxation of constraints, a constraint relaxation necessity detection section detects necessity of constraint relaxation in a problem solving cycle of a problem solving section. When the necessity of constraint relaxation is detected, a relaxation target constraint selection section is enabled to select a constraint to be relaxed from a constraint group. A constraint relaxation section searches a constraint relaxation knowledge management section in association with the selected constraint to check if a partial solution satisfies a relaxation permission condition. If the relaxation permission condition is satisfied, constraint relaxation is attempted according to a relaxation method recorded in correspondence with the relaxation permission condition. When the constraint relaxation is executed, the constraint relaxation necessity detection section checks if the constraint relaxation is successful, and the control returns to the problem solving cycle of the problem solving section.

Abstract: which connict with them are activated. Thus, in example a) of Figure 5, new values for feasible and preferred intervals of Pier-width are found by propagating the constraint from Beam-depth. Preferences represent optimal values, and the closer the value is to the preference the better the criterion is adhered to. When preferences are in connict, they are therefore not dropped, but weakened so that the preferred value becomes the feasible value closest to the interval deened by the preference constraint. Thus, in example b) of Figure 5, the preferred interval of Pier-width is now set to 2.4..2.4], an interval representing the value which is closest to the interval de-ned by the preference constraint. In a later propagation step, this single preferred value may propagate to also x a single value for Beam-depth, as shown in the gure. In both examples of Figure 4 and Figure 5, the label of Beam-depth stays intact even after connict resolution. This assumes that it does not depend on the values for Pier-height and Pier-width. If there is such a dependency, our system follows the truth maintenance algorithm of Doyle (DOY79]) and withdraws the support of all consequences of the revised variables. In the example, the resulting contexts would then be identical to the ones shown, but lack all assertions about the variable Beam-depth which would have to be rededuced. 5 Conclusions We have presented an algorithm for dynamic constraint satisfaction with continous variables, an important problem which has not been addressed in the literature. We have shown that the nature of the problem in continous domains is diierent from discrete domains. In particular, the unbounded nature requires an incremental construction and solution of the constraint network. Contrary to common belief, few published techniques for constraint propagation are applicable to continous domains, and we hope that the topic will receive more attention by the research community in the future. The incremental solution means that the nal results depends essentially on the order in which solutions are generated. Our algorithm provides defaults and preferences as a means to specify heuristics for controlling this ordering. This control is important in view of the fact that realistic design problems are too complex to model domain constraints completely and accurately, and heuristics are necessary to ensure that the result is actually useful. The algorithm we have developed has been implemented as a central element in an intelligent CAD system …

Abstract: Conventional holonomic or nonholonomic constraints are defined as geometric constraints in this paper. If the total energy of a dynamic system can be computed from the initial energy plus the time integral of the energy input rate due to external or internal forces, then the total energy can be artificially treated as a constraint. The violation of the total energy constraint due to numerical errors during simulation can be used as information to control these errors. When geometric constraint control is combined with energy constraint control, numerical simulation of a constrained dynamic system becomes more accurate. An energy constraint control based on the gradient feedback of the energy constraint violation leads to a new method to control both geometric and energy constraint violations, so-called constraint violation stabilization using gradient feedback. A new convenient and effective method to implement energy constraint control in numerical simulation is developed based on the geometric interpretation of the relation between constraints in the phase space. Several combinations of energy constraint control with either Baumgarte's constraint violation stabilization method or the new constraint violation stabilization using gradient feedback are also addressed. Finally, a new method for implementing constraint controls is developed by using the Euler method for integrating constraint control terms, even when higher-order integration methods are used for all other integrations.

Abstract: The author considers the task of designing a control law that forces selected state variables of a linear system to satisfy prescribed algebraic constraint relations and simultaneously guarantees pole placement of the closed-loop system. This task leads to a system representation in semistate form. On the assumption that the system is regular singular, the task is solved in the following steps. The constrained relations are stabilized with prescribed stabilization eigenvalues. Feedback and feedforward controllers that force the control plant to satisfy the constraint relations according to the stabilization dynamics are derived. Implementation conditions of the constraint control laws are derived. The remainder eigenvalues of the constraint control plant that are not fixed by the constraint stabilization are placed by an additional control loop. A constraint separation principle that guarantees an independent choice of the eigenvalues associated with the constraint variables and of those eigenvalues that are associated with the unconstraint variables is proved. The invariance of the stabilized constraint relation under the second control loop is also proved. >

Abstract: In concurrent constraint programming, divergence (i.e. an infinite computation) and failure are often identified. This is undesirable when modelling systems in which infinite behaviour arises naturally. This paper sets out a framework for an axiomatic and denotational view of concurrent constraint programming, and considers the relationship of both views as an instance of Stone duality. We propose a construction of a constraint system which allows both finite and infinite constraints. Subsequently, we provide semantic, topological definitions of safety, liveness and fairness properties in a given constraint system. The process language considered is parametrized by the constraint system. It allows the actions ask and tell, the prefix operator →, the (angelic) non-deterministic choice operator ⊕, the procedure call p(X), and the concurrency operator ∥.

Abstract: A binary resistor network is provided for the labelling of related components of binary or binary-converted images and for artificial vision comprising a plurality of peaks each joined by arches forming binary resistors. Each peak is provided with an elementary processor which enables, with the assistance of a central controller, the association of at least one associative function with each of the arches and a binary constraint with one or more peaks, thus making possible to provide for selective processing of data stored at the site of each of the elementary processors. Each arch of the network is equipped with an associative OR function and forms an accelerated Manchester chain, the establishment time of the network through application of local binary constraints thus being thus linear with the number of peaks.

Abstract: Constraint-based modeling techniques are emerging as an effective computer graphics approach for modeling and designing objects and their behaviors. In this thesis, computer graphics constraint techniques are unified into a single conceptual framework. The central themes of the thesis are methods to partition an arbitrary constraint problem in different domains and at different levels, and to provide a language and computational environment for modeling with constraints. Using partitioning and composition schemes, complex simulations can be built hierarchically from simpler simulations by "plugging" together separate modules. Fundamental and basic structures are designed and implemented to provide an "Assembly Language" for simulation systems. These structures are put together through a collection of interfaces, much like multiple languages that use the same assembler on a computer. We use strategies called refinement and partitioning to integrate seemingly disparate constraint techniques. We present Temporal Sequencing as an approach to design complex time behaviors of simulation systems. Refinement is a top-down approach of transforming high level representations of a constraint modeling problem into representations that are closer to the basic solution mechanisms available in the constraint environment, such as numerical solution methods. Partitioning is the decomposition of one constraint problem into multiple simpler constraint problems that are then studied separately. Temporal Sequencing is a methodology to design the time behavior of a simulation system by composing time behaviors of the system over subintervals of time. Using the above partitioning schemes for the solution and specification of a general constraint problem, we create a unified constraint environment with the capability to both solve constraint problem instances and to create specialized constraint systems. New methods of constraint specification and solution can be added into the same constraint framework as new methods are developed. Based on the above approach, a modeling system called "Our Constraint Environment" (OCE) has been implemented. A programming language as an extension to C++ has been designed to provide an interface to OCE. The language provides the constructs for the partitioning schemes discussed above. Simulations created using OCE have shown the efficacy of our design approach. Constraint-based modeling techniques are emerging as an effective computer graphics approach for modeling and designing objects and their behaviors. In this thesis, computer graphics constraint techniques are unified into a single conceptual framework. The central themes of the thesis are methods to partition an arbitrary constraint problem in different domains and at different levels, and to provide a language and computational environment for modeling with constraints. Using partitioning and composition schemes, complex simulations can be built hierarchically from simpler simula

Abstract: The purpose of the presented research is to study the convergence characteristics of Hopfield network dynamics. The relation between constraint weight parameter values and the stability of solutions of constraint satisfaction and optimization problems mapped to Hopfield networks is investigated. A theoretical development relating constraint weight parameter values to solution stability is presented. The dependency of solution stability on constraint weight parameter values is shown employing an abstract optimization problem. A theorem defining bounds on the constraint weight parameter magnitudes for solution stability of constraint satisfaction and optimization problems is proved. Simulation analysis on a set of optimization and constraint satisfaction problems to test and verify the theoretical findings are performed.

Abstract: The paper demonstrates how geometrical constraints can be applied to add a new level of abstraction to description of geometrical objects. Special attention is given to the interactive insertion of constraints. To support incremental design each inserted constraint has to be solved as soon as possible. Because of this requirement a local propagation of known states is used for constraint solving. It is supported by a biconnected constraint description graph structure. The benefits of this structure are insensibility to the order of inserted constraints and ability of replacing constraints with their inverse couples. To override the ambiguities at constraint solving the approximal values of geometrical elements which are inserted through a sketch are used. From the biconnected constraint description graph an acyclic constraint description graph is generated easily. It is suitable for the generation of instances of generic objects.

Abstract: We show that it is possible to transform any given LPO ordering constraint C into a finite equivalent set of constraints S for which a special kind of solutions can be obtained. This allows to compute the equalities that follow from ordering constraints, and to decide e.g. whether an ordering constrained equation is a tautology. Another application we develop here is a method to check ordered rewrite systems for (ground) confluence. •This work has been done during a half-year stay at the Max-Planck-lnstitut fiir Informatik, Im Stadtwald, D-W-6600 Saarbriicken, Germany. Author's Permanent address: Technical University of Catalonia, Pau Gargallo 5, 08028 Barcelona, Spain. E-mail: robertoCilsi. upc. es.

Abstract: We present our constraint-based geometric modeling system named FLEXI. Creation of an object begins with a sketch carrying a topological information and approximal values of object’s geometry. Geometrical constraints are then interactively inserted. Benefits of the presented geometric modeling system are unnecessity of giving constraints in correct order and the ability of replacing incorrect constraints with their inverse constraints by the system itself. Special attention is given to the iterative constraint solving. A new structure - a biconnected constraint description graph enables these benefits. A triggering mechanism for controlling of the constraint propagation is developed for this structure. An algorithm for converting the biconnected constraint description graph into an acyclic constraint description graph is briefly explained. Managing of the over-dimensioning is solved by introduction of a priority mechanism.

Abstract: Symbolic and numerical techniques are coupled together in a proposed geometric modeling system. The geometric modeling system is based on geometrical constraints. It is unnecessary to give constraints in the correct order and the ability of replacing incorrect constraints with their inverse constraints exists in the system itself. A new structure, a biconnected constraint description graph, is used. A triggering mechanism for controlling of the constraint propagation is developed for this structure. An algorithm for converting the biconnected constraint description graph into an acyclic constraint description graph is outlined. >

Abstract: The invention relates to a network of binary resistors. The network comprises a plurality of vertices (Soi, j) each linked by arcs a forming binary resistors. Each vertex comprises an elementary processor (PEi, j) making it possible, from a central controller (C) to associate with each of the arcs at least one associative function and with one or more vertices, a binary constraint (F1, F2) making it possible to provide for selective processing of data stored in the region of each of the elementary processors. Each arc of the network is equipped with an associated OR function, by means of each elementary processor. Application to the labelling of related components of binary or digitised images and to artificial vision.

Abstract: The authors recall the constraint programming approach to solving a constraint-satisfaction problem, and show that for each problem which can be described by this approach a neural network can be designed which solves the problem. They give an application of this method for solving a task assignment problem and compare the results with those which are obtained by other approaches. Because this network can be very large, a type of constraint which allows splitting the problem into two smaller problems is illustrated. >

Abstract: The paper proposes a new approach to reduce a constraint network so that a backtrack-free search may be used, based on local consistency. It shows that this approach can be used to solve efficiently a large class of the constraint satisfaction problem. >

Abstract: In this paper we propose a novel computational model for constraint logic programming (CLP) languages. The model provides an efficient mechanism for executing CLP programs by exploiting constraint satis¬faction as a means for both solving constraints and controlling the whole computation. In the model, we separate constraint solving from the de-duction procedure. Deductions over constraints are extracted from the source program and represented as a context-free grammar that encodes the way in which deduction will generate constraints to be solved. There-fore, deduction is performed abstractly at compile time. Executing the grammar generates all the constraints that need to be solved at run time. A very flexible control mechanism is therefore provided by the model in terms of the information fed back from the constraint solving procedure. It is shown that the model provides a general scheme for investigating an efficient computational model for implementing constraint logic pro-gramming systems.

Abstract: Conventional constraint systems are suitable for finding assignments to a finite set of parameters such that a set of constraints are satisfied. However, in generalized problem-solving, the set of parameters for which values must be found is only a subset of a much larger (possibly infinite) set of parameters, and the membership of this subset is dependent on conditions whose truth or falsity can only be determined dynamically. Conventional constraint systems are not suitable for such problems because conventional constraint processing requires that the set of parameters for which values are to be found should be fixed a priori. In this paper, we show how the conventional notion of constraint processing can be generalized to address the broader class of problem mentioned above.

Abstract: The paper introduces three scalable static parallel arc consistency algorithms (SPAC-1, SPAC-2 and SPAC-3) designed for any general-purpose shared memory multiple instruction-stream, multiple data-stream (MIMD) computer. The algorithms are intended for constraint satisfaction problems in AI applications. Arc consistency is ensured of a finite domain binary constraint network. Through actual machine experimentation the paper measures work performed by the SPAC algorithms and compares it with work performed by existing sequential algorithms, AC-1 and AC-3. Results shows that the parallel arc consistency algorithms can be effectively used to pre-process a constraint network. >

Abstract: Uniform representation for assembly constraints that applies to a wide variety of constraint relations given in the literature is given. A systematic procedure for constraint reduction is also given: if two parts or subassemblies are related by multiple constraints, the constraint reduction procedure computes a single net constraint having the same effect. Three broad applications of the constraint representation and constraint reduction methods to problems in assembly modeling and tolerancing are discussed. >