Publications

 The super-dense computation model provides an abstraction of real-time behaviour of computing systems. Logics to deal with this model are being studied. In the paper, we propose a combination of a linear temporal logic and an interval logic, and demonstrate how this combination can be used to specify a real-time semantics of an OCCAM-like programming language and its real-time properties, where the super-dense computation model is adopted.

 The research on hybrid control systems attracts many scientists both in computer science and control theories and applications. The study should be carried out on a general framework abstracted from various hybrid control systems. This paper analyses the drawbacks of the present frameworks used by most researchers and proposes a new framework to overcome these shortcomes. The new framework consists of a discrete time box, a discrete event box and a digital-symbol interface. The new framework shows the crucial nature of the hybridity of time envolving variables and event driven variables in hybrid control systems. The new framework is easy to integrate the knowledges of computer science and control theories and applications. Two examples, a gas burner and an inverse pendulum are given to show the fitness of the new framework. The design and analysis aspects of hybrid control systems related to the new framework are also discussed.

 Most results obtained in the research of hybrid control systems are related to the description and analysis of hybrid control systems. But it is doubtless that how to design a hybrid control system is of great significance in the research of hybrid control systems. This paper is devoted to discuss the design methodology of hybrid control systems. After an introduction of a new framework of hybrid control systems, a top-down design approach is proposed which is consistent to the framework. The approach consists of decomposition of system performance specifications, the design of discrete event driven decision maker and the design of digital control loops. Two examples, a gas burner and an inverse pendulum are systematically designed to show the goodness of the top-down design approach. Finally, a bottom-up analysis approach which is consistent to the new framework is proposed and then applied to these examples.

Theories of graphs and graph transformations form an important part of the mathematical foundations of computing, and have been applied in a wide range of areas from the design and analysis of algorithms to the formalization of various computer systems and programs. In this thesis, we study how graphs and graph transformations can be used to model the static structure and dynamic behavior of object-orientated and service-oriented systems.

Our work is mainly motivated by the difficulty in understanding and reasoning about object-orientated and service-oriented programs, which have more sophisticated features compared with traditional procedural programs. We show that the use of graphs and graph transformations provides both an intuitive visualization and a formal representation of object-orientated and service-oriented programs with these features, improving people’s understanding of the execution states and behaviors of these programs.

We provide a graph-based type system, operational semantics and refinement calculus for an object-oriented language. In this framework, we define class structures and execution states of oo programs as directed and labeled graphs, called class graphs and state graphs, respectively. The type system checks whether a program is well-typed based on its class graph, while the operational semantics defines each step of program execution as a simple graph transformations between state graphs. We show the operational semantics is type-safe in that the execution of a well-typed program does not “go wrong”. Based on the operational semantics, we study the notion of structure refinement of oo programs as graph transformations between their class graphs. We provide a few groups of refinement rules for various purposes such as class expansion and polymorphism elimination and prove their soundness and relative completeness.

We also propose a graph-based representation of service-oriented systems specified in a service-oriented process calculus. In this framework, we define states of service-oriented systems as hierarchical graphs that naturally capture the hierarchical nature of service structures. For this, we exploit a suitable graph algebra and set up a hierarchical graph model, in which graph transformations are studied following the well-known Double-Pushout approach. Based on this model, we provide a graph transformation system with a few sets of graph transformation rules for various purposes such as process copy and process reduction. We prove that the graph transformation system is sound and complete with respect to the reduction semantics of the calculus.

 Business Process Execution Language (BPEL), or Web Services BPEL (WS-BPEL), is the standard for specifying workflow process definition using web services. Research on formal modelling and verification of BPEL has largely concentrated on control flow and data flow, while security related properties have received little attention. In this work, we present a formal framework that integrates Role Based Access Control (RBAC) into BPEL and allows us to express authorisation constraints using temporal logic. Using this framework, we show how model-checking can be applied to verify that a given BPEL process satisfies the security constraints.

Being a successful technique in software practice, object orientation (OO) is a hot topic in academic research fields. Among many formalisms, rCOS, a refinement calculus of object-oriented systems based on unifying theories of programming (UTP), has been proven a promising one in the sense of its applications to incremental software constructions, the formal use of UML, etc. However, equipped with a semantics reasoning on both static and dynamic properties, rCOS is not designed for static checking. We believe introducing static checking will extend the power of rCOS. In this paper, we develop a type system for rCOS and prove some type safety theorems. To make the theoretical results of this paper convincible and easy to be understood, we follow the traditional approaches of type systems construction. That is, we use an operational semantics as the basic explanation of rCOS language in spite of the fact that rCOS is originally developed in a denotational framework.

An object-oriented program consists of a section of class declarations and a main method. The class declaration section represents the structure of an object-oriented program, that is the data, the classes and relations among them. The execution of the main method realizes the application by invoking methods of objects of the classes defined in the class declarations. Class declarations define the general properties of objects and how they collaborate with each other in realizing the application task programmed as the main method. Note that for one class declaration section, different main methods can be programmed for different applications, and this is an important feature of reuse in object-oriented programming. On the other hand, different class declaration sections may support the same applications, but these different class declaration sections can make significant difference with regards to understanding, reuse and maintainability of the applications. With a UML-like modeling language, the class declaration section of a program is represented as a class diagram, and the instances of the class diagram are represented by object diagrams, that form the state space of the program. In this paper, we define a class diagram and its object diagrams asdirected labeled graphs, and investigate what changes in the class structure maintain the capability of providing functionalities (or services). We formalize such a structure change by the notion of structure refinement. A structure refinement is a transformation from one graph to another that preserves the capability of providing services, that is, the resulting class graph should be able to provide at least as many, and as good, services (in terms of functional refinement) as the original graph. We then develop a calculus of object-oriented refinement, as an extension to the classical theory of data refinement, in which the refinement rules are classified into four categories according to their natures and uses in object-oriented software design. The soundness of the calculus is proved and the completeness of the refinement rules of each category is established with regard to normal forms defined for object-oriented programs. These completeness results show the power of the simple refinement rules. The normal forms and the completeness results together capture the essence of polymorphism, dynamic method binding and object sharing by references in object-oriented computation. 

 In this paper we present a pomset semantics for a shared-variable parallel language which is an extension of the one studied by Brookes in [5]. The pomset semantics lifts the transition trace semantics to the non-interleaving setting, where parallel events in a pomset transition trace are labeled by conditionally independent actions. Most of the important laws from the interleaving setting also hold in the non-interleaving setting. Similarities and differences with other related works are discussed.

 An object-oriented program consists of a section of class declarations and a main method. The class declaration section represents the structure of an object-oriented program, that is the data, the classes and relations among them. The execution of the main method realizes the application by invoking methods of objects of the classes defined in the class declarations. Class decorations define the general properties of objects and how they collaborate with each other in realizing the application task programmed as the main method. Note that for one class declaration section, different main methods can be programmed for different applications, and this is an important feature of reuse in object-oriented programming. On the other hand, different class declaration sections may support the same applications, but these different class declaration sections can make significant difference with regards to understanding, reuse and maintainability of the applications. With a UML-like modeling language, the class declaration section of a program is represented as a class diagram, and the instances of the class diagram are represented by object diagrams, that form the state space of the program. In this paper, we define a class diagram and its object diagrams as directed labeled graphs, and investigate what changes in the class structure maintain the capability of providing functionalities (or services). We formalize such as structure change by the notion of structure refinement. A structure refinement is a transformation from one graph to another that preserves the capability of providing services, that is, the resulting class graph should be able to provide at least as many, and as good, services (in terms of functional refinement) as the original graph. We then develop a calculus of object-oriented refinement in which the refinement rules are classified into four categories according to their natures and uses in object-oriented software design. The soundness of the calculus is proved and the completeness of the refinement rules of each category is established with regard to normal forms defined for object-oriented programs. These completeness results show the power of the simple refinement rules. The normal forms and the completeness results together capture the essence of polymorphism, dynamic method binding and object sharing by references in object-oriented computation. Keywords: Class graph, Object graph, Graph transformation, Normal form, Object-orientation, Structure refinement.

 Preliminary proceedings of the papers presented at the TTSS'08 workshop for the convenience of the workshop participants. A selection of revised papers will be published in Electronic Notes in Theoretical Computer Science by Elsevier.

 Being a successful technique in software practice, Object Orientation (OO) is a hot topic in academic research fields. Among many formalisms, rCOS, a refinement calculus of object-oriented systems based on Unifying Theories of Programming (UTP), has been proven a promising one in the sense of its applications to incremental software constructions, the formal use of UML, etc. However, equipped with a semantics reasoning on both static and dynamic properties, rCOS is not designed for static checking. We believe introducing static checking will extend the power of rCOS. In this paper, we develop a type system for rCOS and prove some type safety theorems. To make the theoretical results of this paper convincible and easy to be understood, we follow the traditional approaches of type systems construction. That is, we use an operational semantics as the basic explanation of rCOS language in spite of the fact that rCOS is originally developed in a denotational framework.