An intermediate-level specification notation is presented for use with BSP-style programming. It is achieved by extending pre-post semantics to reveal state at points of global synchronisation. That enables us to integrate the pre-post, finite and reactive-process styles of specification in BSP, as shown by our treatment of the dining philosophers. The language is provided with a complete set of laws and has been formulated to benefit from a simple predicative semantics.

In this paper we use the concept of resource cumulation to model various forms of computation. The space of cumulations (called a cumulator) is simply represented as a five tuple consisting of a well-founded partial order, a monoid and a volume function. The volume function is introduced to simplify reasoning about limit points and other topological properties. A specification command is a set of cumulations. Typical phenomena of concurrency such as reactiveness, safety and liveness, fairness, real time and branching time naturally arise from the model. In order to support a programming theory, we introduce a specification language that incorporates sequentiality, nondeterminism, simple parallelism, negation and general recursions. A new fixpoint technique is used to model general recursions. The language is applied to the case study on CSP, which becomes a special model of cumulative computing with a combination of four resource cumulators of alphabet, termination, trace and refusal. All laws of cumulative computing are also valid for CSP and the generalization from CSP to Timed CSP can be achieved by simply combining the four cumulators with real time. Loops whose bodies may take zero time can then be modeled more satisfactorily. 1

This paper studies top-down program development techniques for BulkSynchronous Parallelism. In that context a specification formalism Logs, for `the Logic of Global Synchrony', has been proposed for the specification and high-level development of BSP designs. This paper extends the use of Logs to provide support for the protection of local variables in BSP programs, thus completing the link between specifications and programs.

In this paper we develop a new model for objects with references. Each object is represented as a set of "threads" each of which contains an entry, an exit and a sequence of attributes. The entries and exits are the abstraction of references. Garbage collection can be easily defined. Knowledge about the operators are summarized as algebraic laws. The model is then applied to define the semantics of a prototype object-oriented language. The language incorporates classes, single inheritance, dynamic type checking, error handling, and method calls.

In computer science fixpoints play a crucial role. Most often least and greatest fixpoints are sufficient. However there are situations where other ones are needed. In this paper we study, on an algebraic base, a special fixpoint of the function f (x) = a · x that describes infinite iteration of an element a. We show that the greatest fixpoint is too imprecise. Special problems arise if the iterated element contains the possibility of stepping on the spot (e.g. skip in a programming language) or if it allows Zeno behaviour. We present a construction for a fixpoint that captures these phenomena in a precise way. The theory is presented and motivated using an example from hybrid system analysis.