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. 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

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This paper provides a systematic and full treatment of mode transfer operators in process algebra, including complete axiomatizations, operational rules, analysis of expressive power and extensions with timing features. In particular, we study a disrupt operator and an interrupt operator. Note: this paper is a revision and extension of [7] 1 Introduction A useful feature in programming languages and specification languages is the ability to denote mode switches. In particular, most languages have means to describe the disrupt or interrupt the normal execution of a system. Also in process algebra, various disrupt and interrupt operators have received attention, see e.g. [7], [10], [11], [3], [12]. In LOTOS (see [9]) we have the disruption operator, that is denoted [>. Another name is disabling. In this paper, we provide a systematic and full treatment of mode transfer operators in process algebra, including complete axiomatizations, operational rules, analysis of expressive power and ...

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.

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.

Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about well-behaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various kinds of operational descriptions in a uniform fashion. In this paper, bialgebraic semantics is combined with a coalgebraic approach to modal logic in a novel, general approach to proving the compositionality of process equivalences for languages defined by structural operational semantics. To prove compositionality, one provides a notion of behaviour for logical formulas, and defines an SOS-like specification of modal operators which reflects the original SOS specification of the language. This approach can be used to define SOS congruence formats as well as to prove compositionality for specific languages and equivalences. Key words: structural operational semantics, coalgebra, bialgebra, modal logic, congruence format 1

More than a decade ago, Moller and Tofts published their seminal work on relating processes that are annotated with lower time bounds, with respect to speed. Their paper has left open many questions concerning the semantic theory for their suggested bisimulation-based faster-than preorder, the MT-preorder, which have not been addressed since. The encountered difficulties concern a general compositionality result, a complete axiom system for finite processes, and a convincing intuitive justification of the MT-preorder. This paper solves these difficulties by developing and employing novel tools for reasoning in discrete-time process algebra, in particular a general commutation lemma relating the sequencing of action and clock transitions. Most importantly, it is proved that the MT–preorder is fully-abstract with respect to a natural amortized preorder that uses a simple bookkeeping mechanism for deciding whether one process is faster than another. Together these results reveal the intuitive roots of the MT-preorder as a faster–than relation, while testifying to its semantic elegance. This lifts some of the barriers that have so far hampered progress in semantic theories for comparing the speed of processes.

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.

In the paper we present an ACP-like process algebra which can be used to model both probabilistic and time behaviour of parallel systems. This process algebra is obtained by extension of untimed probabilistic process algebra with constructors that allow the explicit specification of timing aspects. In this paper we concentrate on giving axioms and deduction rules for these constructors. We give two probabilistic process algebras with discrete time. The first one only manipulates with processes that may be initialized within the current time slice or may delay a finite and fixed number of time slices. Later, we add processes whose execution can be postponed for an arbitrary number of time slices.