Abstract. We propose a process algebra obtained by extending a combination of the process algebra with continuous relative timing from Baeten and Middelburg [Process Algebra with Timing, Springer, Chap. 4, 2002] and the process algebra with propositional signals from Baeten and

While studying the specification of the operational semantics of different programming languages and formalisms, one can observe the following three facts. Firstly, Plotkin’s style of Structured Operational Semantics (SOS) has become a standard in defining operational semantics. Secondly, congruence with respect to some notion of bisimilarity is an interesting property for such languages and it is essential in reasoning about them. Thirdly, there are numerous languages that contain an explicit data part in the state of the operational semantics. The first two facts, have resulted in a line of research exploring syntactic formats of operational rules to derive the desired congruence property for free. However, the third point (in combination with the first two) is not sufficiently addressed and there is no standard congruence format for operational semantics with an explicit data state. In this paper, we address this problem by studying the implications of the presence of a data state on the notion of bisimilarity. Furthermore, we propose a number of formats for congruence. 1

Certain principles are fundamental to operational semantics, regardless of the languages or idioms involved. Such principles include rule-based definitions and proof techniques for congruence results. We formulate these principles in the general context of categorical logic. From this general formulation we recover precise results for particular language idioms by interpreting the logic in particular categories. For instance, results for first-order calculi, such as CCS, arise from considering the general results in the category of sets. Results for languages involving substitution and name generation, such as the π-calculus, arise from considering the general results in categories of sheaves and group actions. As an extended example, we develop a tyft/tyxt-like rule format for open bisimulation in the π-calculus.

We propose a variant of the version of branching bisimulation equivalence for processes with discrete relative timing from Baeten, Bergstra, and Reniers. We show that this new equivalence allows for the functional correctness of the PAR protocol as well as its performance properties to be analyzed. The new equivalence still coincides with the original version of branching bisimulation equivalence from van Glabbeek and Weijland in the case without timing.

In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [62]. Subsequently, the format of SOS rules became the object of study. Using so-called Transition System Specifications (TSS’s) several authors syntactically restricted the format of rules and showed several useful properties about the semantics induced by any TSS adhering to the format. This has resulted in a line of research proposing several syntactical rule formats and associated meta-theorems. Properties that are guaranteed by such rule formats range from well-definedness of the operational semantics and compositionality of behavioral equivalences to security- and probability-related issues. In this paper, we provide an initial hierarchy of SOS rules formats and meta-theorems formulated around them.

In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [G.D. Plotkin, A structural approach to operational semantics, Technical

Abstract. The possibility of two or more actions to be performed consecutively at the same point in time is not excluded in the process algebras from the framework of process algebras with timing presented by Baeten and Middelburg [Handbook of Process Algebra, Elsevier, 2001, Chapter 10]. This possibility is useful in practice when describing and analyzing systems in which actions occur that are entirely independent. However, it is an abstraction of reality to assume that actions can be performed consecutively at the same point in time. In this paper, we propose a process algebra with timing in which this possibility is excluded, but the finite elements of the nonstandard extension of the non-negative real numbers are taken as time domain. It is shown that this new process algebra generalizes the process algebras with timing from the aforementioned framework in a smooth and natural way.

Abstract. We investigate the connections between the process algebra for hybrid systems of Bergstra and Middelburg and the formalism of hybrid automata of Henzinger et al. We give interpretations of hybrid automata in the process algebra for hybrid systems and compare them with the standard interpretation of hybrid automata as timed transition systems. We also relate the synchronized product operator on hybrid automata to the parallel composition operator of the process algebra. It turns out that the formalism of hybrid automata matches a fragment of the process algebra for hybrid systems closely. We present an adaptation of the formalism of hybrid automata that yields an exact match.

Abstract. We propose a process algebra obtained by adapting the process algebra with continuous relative timing from Baeten and Middelburg [Process Algebra with Timing, Springer, Chap. 4, 2002] to spatially located actions. This process algebra makes it possible to deal with the behaviour of systems with a known time-dependent spatial distribution, such as a protocol transmitting data via a mobile intermediate station. It is a reformulation of the real space process algebra from Baeten and Bergstra [Formal Aspects of Computing 5:481–529, 1993] in a setting with urgent actions. This leads to many simplifications.

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