We investigate different forms of termination in timed process algebras. The integrated framework of discrete and dense time, relative and absolute time process algebras is extended with forms of successful and unsuccessful termination. The different algebras are interrelated by embeddings and conservative extensions.

Abstract. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The author gives his personal views on these matters. He also considers the present situation, and states some challenges for the future.

Timed algebraic process theories can be developed with quite different purposes in mind. One can aim for theoretical results about the theory itself (completeness, expressiveness, decidability), or one can aim for practical applicability to non-trivial protocols. Unfortunately, these aims do not go well together. In this paper we take two theories, which are probably of the first kind, and try to find out how well suited they are for practical verifications. We verify Fischer's protocol for mutual exclusion in the settings of discrete-time process algebra (ACP dt ) and real-time process algebra (ACP ur ). We do this by transforming the recursive specification into an equivalent linear specification, and then dividing out the maximal bisimulation relation. The required mutual exclusion result can then be found by reasoning about the obtained process graph. Finally, we consider the ease of the verification, and ways to adapt the theory to make it more practical. It will turn out that the...

TTCN (Tree and Tabular Combined Notation) is the standardized test notation for the description of OSI conformance tests. Since applicability of TTCN is restricted, work on the definition of concurrent TTCN, an extended version of TTCN for the specification of test cases for multi party testing, has been started a few years ago. In this paper we discuss different approaches for the definition of an operational semantics of TTCN and concurrent TTCN and we discuss issues related to the validation of (concurrent) TTCN test cases. Because for the validation of test cases a proper semantics definition is a prerequisite we have developed a semantics definition which utilizes labelled transition systems as its basic model. The applicability of the model is demonstrated: First, we show how identified incompletenesses and ambiguities of TTCN can be solved. Second, we develop a validation framework that defines the necessary machinery for the validation of functional properties of test ...

. We present an !-complete algebra of a class of deterministic event structures, which are labelled prime event structures where the labelling function satisfies a certain distinctness condition. The operators of the algebra are summation, sequential composition and join. Each of these gives rise to a monoid; in addition a number of distributivity properties hold. Summation loosely corresponds to choice and join to parallel composition, with however some nonstandard aspects. The space of models is a complete partial order (in fact a complete lattice) in which all operators are continuous; hence minimal fixpoints can be defined inductively. Moreover, the submodel relation can be captured within the algebra by summation (x v y iff x + y = y); therefore the effect of fixpoints can be captured by an infinitary proof rule, yielding a complete proof system for recursively defined deterministic event structures. 1 Introduction It is generally recognised that prime event structures constitut...

Abstract. We treat theory and application of timed process algebra. We focus on a variant that uses explicit termination and action prefixing. This variant has some advantages over other variants. We concentrate on relative timing, but the treatment of absolute timing is similar. We treat both discrete and dense timing. We build up the theory incrementally. The different algebras are interrelated by embeddings and conservative extensions. As an example, we consider the PAR communication protocol. 1