An algebraic approach to data languages and timed languages

Algebra offers an elegant and powerful approach to understand regular languages and finite automata. Such framework has been notoriously lacking for timed languages and timed automata. We introduce the notion of monoid recognizability for data languages, which includes timed languages as special case, in a way that respects the spirit of the classical situation. We study closure properties and hierarchies in this model and prove that emptiness is decidable under natural hypotheses. Our class of recognizable languages properly includes many families of deterministic timed languages that have been proposed until now, and the same holds for non-deterministic versions.     

An algebraic model for programming languages

The language of universal algebras is used as a model for programming language specification. BNF rules are employed for specifying the signature of the language algebra instead of the context free syntax. The algorithm for program evaluation is inductively defined by the following universal algebraic construction:

Any function defined on the generators of a free algebra taking values in the carrier of another similar algebra can be uniquely extended to a homomorphism between the two algebras.

Any conventional programming language can be specified by a finite set of BNF rules and its algebra of symbols is generated by a finite set of generator classes. Thus any function defined on the finite set of generators offers an algebraic mechanism for a universal algorithm for source language program evaluation.     

An object-oriented approach for mechanical components design and visualization

In this paper, development of shape modeling tools for engineering design, analysis, simulation, and visualization is presented. The approach based on the idea of function-based shape modeling is combined with the power and versatility of the object-oriented programming (OOP). An OOP code, initially developed as a teaching and learning tool for educational use in an undergraduate Modeling and Simulation course, to generate mechanism components is presented. Different parametric, explicit, and implicit functions or their combination are used to generate mechanical components shapes. Using a blending process, sophisticated shapes have been generated on the graphical interface. However, the ideas and concept of the OOP mechanical components design presented in this paper can be applied to other application areas.     

An algebraic theory of object-oriented systems

The paper presents an algebraic specification of net objects. By net objects we mean those that are defined in object-oriented paradigms and those defined with nested relations in complex database models. An algebraic specification is set up that involves structures of net objects, accesses of net objects, and some features of object-oriented programming, such as multiple inheritance and polymorphism. Objects and their relationships are then characterized formally in the modeling, which utilizes the hierarchical approach in the algebraic theory of abstract data types, and is further developed by adding mechanisms from existing object systems. Categories of net objects are presented with the properties of accesses among them     

An object-oriented approach to the design of a mail system for a heterogeneous environment

The design of an electronic mail system, MASH, is presented in this paper. The system, to be used in a heterogeneous environment, provides common user interfaces that allow the use of several diverse workstations. It also allows message transmission through different networks. An object-oriented approach is adopted to model the handling of the user interface and communication. This approach results in procedural transparency to users when using the system.     

An object-oriented approach to computer-aided design of a plastic injection mould

This paper describes a knowledge-based and object-oriented approach for the design of the feed system for plastic injection moulds. The gating system of a plastic injection mould plays a significant role in producing a quality part. Designing of this gating system entails a great amount of effort from an experienced designer and it is time-consuming. CADFEED (Computer-Aided Design of the FEED system of the plastic injection mould) is developed to accurately and efficiently design the type, location and size of a gating system of a plastic injection mould. This system provides an accurate and fast means of obtaining solutions based on the users' requirements, which are easily handled by the rating algorithm in the system. CADFEED generates acceptable solutions at a lower cost than most traditionally and commercially available analysis packages. This system can be used to verify designs proposed by the design engineers. It can also help novice engineers in the understanding of mould design. Another important feature of CADFEED is that it is a low cost system, which uses AutoCAD and an expert system shell on a personal computer. This feature makes CADFEED easily affordable by small-scale industries.     

An object-oriented approach to application generation

The TUBA system consists of a set of integrated tools for the generation of business-oriented applications. Tools and applications have a modular structure, represented by class objects. The article describes the architecture of the environments for file processing, screen handling and report writing.     

An object-oriented approach to Computer Integrated Systems

In recent years computers have been incorporated into large scale systems such as nuclear plant, flight control, and manufacturing systems. Such Computer Integrated Systems (CIS) normally consist of heterogeneous subsystems. The integration of heterogeneous subsystems requires that the subsystems be portable, inter-operable, and integrable at both software and hardware levels so that the integrated system should function properly. Objects and nets are proposed as the atomic elements of CIS's. An object is defined as a computational model of an arbitrary entity. Then three representation schemes of an object are introduced: algebraic, modular, and graphical. Two operations on objects,Composition andUnion, are introduced as means of combining two objects into a larger one. As an application of this approach, a Computer Integrated Manufacturing (CIM) system is represented as a network of objects.     

An algebraic approach to shape-from-image problems

This paper presents a new method for recovering three-dimensional shapes of polyhedral objects from their single-view images. The problem of recovery is formulated in a constrained optimization problem, in which the constraints reflect the assumption that the scene is composed of polyhedral objects, and the objective function to be minimized is a weighted sum of quadric errors of surface information such as shading and texture. For practical purpose it is decomposed into the two more tractable problems: a linear programming problem and an unconstrained optimization problem. In the present method the global constraints placed by the polyhedron assumption are represented in terms of linear algebra, whereas similar constraints have usually been represented in terms of a gradient space. Moreover, superstrictness of the constraints can be circumvented by a new concept ‘position-free incidence structure’. For this reason the present method has several advantages: it can recover the polyhedral shape even if image data are incorrect due to vertex-position errors, it can deal with perspective projection as well as orthographic projection, the number of variables in the optimization problem is very small (three or a little greater than three), and any kinds of surface information can be incorporated in a unifying manner.     

An algebraic approach to supervisory control

Supervisory control problems are formulated in terms of a process model where the mechanism of control is expressed in terms of an algebraic operator with the plant and supervision processes as its arguments. The solution subspaces for supervisory processes restrict the observation and the control capability of supervision. The main result corresponds to decentralized marked supervision under partial observations, and specific cases are derived from this result in a unified, algebraic way. The result and its derivation demonstrate the relative simplicity of the algebraic process formulation.     

An algebraic approach to feature interactions

The various approaches proposed to provide communication between CAD systems and process planning systems share the major problem that, due to geometric interactions among features, there may be several equally valid sets of manufacturable features describing the same part, and different sets of features may differ in their manufacturability. Thus, to produce a good process plan-or, in some cases, any plan at ll-it may be necessary to interpret the part as a different set of features than the one initially obtained from the CAD model. This is addressed using an algebra of features. Given a set of features describing a machinable part, other equally valid interpretations of the part can be produced by performing operations in the algebra. This will enable automated process planning systems to examine these interpretations in order to see which one is most appropriate for use in manufacturing. The feature algebra has been implemented for a restricted domain and integrated with the Protosolid solid modeling system and the EFHA process planning system     

Constraint maintenance in engineering design system: An active object-oriented approach

This paper proposes a framework of engineering constraint maintenance using an active object-oriented database and solves a problem encountered when implementing the framework. The framework is proposed for the information-driven CIM system that integrates engineering constraints as well as its data. It resolves problems of the existing application-oriented constraint maintenance in which constraints are scattered in heterogeneous applications. It is possible due to the integrated management of constraints on a database using triggers, that is, on an “active” database. Existing active object-oriented databases, however, cannot properly support certain constraints that are specified on a set of classes. Those are the cases where the constraints must be maintained in the forward direction along a class composition hierarchy as well as in the backward direction. We call these kinds of problems “backward propagation problems” and investigate several approaches to resolve them using currently available techniques. Based on an approach which uses virtual classes, a new constructor, called CONSTRAINT^CCH is proposed to support the backward propagation. Advantages of the proposed framework and the constructor for the backward propagation are demonstrated on a design constraint management that supports a control panel design.     

An object-oriented approach to the solid modeling of empirical data

An object-oriented approach to the construction, manipulation, and display of complex geometric models of oil reservoirs is described. The authors have extended the traditional constructive solid geometry modeling techniques to accommodate the requirements for reservoir models. Both the user interface and the model building are implemented in Strobe, an object-oriented extension to Interlisp. The geometric model is specified through a CSG-graph editor built using an object-oriented toolkit for graphical interfaces. This editor proves to be an invaluable tool with which to build, maintain and manipulate large, complicated geometric models     

An object-oriented manufacturing scheduling approach

Scheduling is the process of devising or designing a procedure for a particular objective. Because of the dynamic domains that certain scheduling systems must solve, we have proposed an eight layer scheduling model that would aid in developing general scheduling systems. In the article our model is presented together with current scheduling systems researched. From these systems we have developed an object-oriented scheduling system, which is described from the design phase to the object implementation phase     

An algebraic approach to continuous collision detection for ellipsoids

We present algebraic expressions for characterizing three configurations formed by two ellipsoids in R³ that are relevant to collision detection: separation, external touching and overlapping. These conditions are given in terms of explicit formulae expressed by the subresultant sequence of the characteristic polynomial of the two ellipsoids and its derivative. For any two ellipsoids, the signs of these formulae can easily be evaluated to classify their configuration. Furthermore, based on these algebraic conditions, an efficient method is developed for continuous collision detection of two moving ellipsoids under arbitrary motions.     

An algebraic approach to iterative learning control

In this paper discrete-time iterative learning control (ILC) systems are analysed from an algebraic point of view. The algebraic analysis shows that a linear-time invariant single-input–single-output model can always represented equivalently as a static multivariable plant due to the finiteness of the time-axis. Furthermore, in this framework the ILC synthesis problem becomes a tracking problem of a multi-channel step-function. The internal model principle states that for asymptotic tracking (i.e. convergent learning) it is required that an ILC algorithm has to contain an integrator along the iteration axis, but at the same time the resulting closed-loop system should be stable. The question of stability can then be answered by analysing the closed-loop poles along the iteration axis using standard results from multivariable polynomial systems theory. This convergence theory suggests that time-varying ILC control laws should be typically used instead of time-invariant control laws in order to guarantee good transient tracking behaviour. Based on this suggestion a new adaptive ILC algorithm is derived, which results in monotonic convergence for an arbitrary linear discrete-time plant. This adaptive algorithm also has important implications in terms of future research work—as a concrete example it demonstrates that ILC algorithms containing adaptive and time-varying components can result in enhanced convergence properties when compared to fixed parameter ILC algorithms. Hence it can be expected that further research on adaptive learning mechanisms will provide a new useful source of high-performance ILC algorithms.     

An object-oriented approach to teaching mathematics for engineering and science students

It is suggested to teach mathematics for engineering and science students as exploration of mathematics-related classes. Similarity with classes and objects of object-oriented programming is demonstrated. In the framework of the suggested approach, each relatively self-contained unit of mathematics curriculum is assigned a data type and is considered a class. In such setting, a theorem proof may be viewed as an assignment of values to object properties. The approach augments the role of recognition of mathematical objects, their properties and methods （operations） and diminishes the value of comprehensive study of rigorous proofs. The approach emphasizes the importance of development of mathematical intuition and combines conceptual and operational approaches to teaching and learning mathematics. Prospective implementation assumes using of computer-based systems of formal proof.