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.

This chapter surveys the semantic rami cations of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. The need for these enriched formalisms arises when one wishes to model system features such asinterrupts, prioritized choice, orreal-time behavior. Approaches to priority in process algebras can be classi ed according to whether the induced notion of pre-emption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global preemption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the e cient encoding of real-time semantics. Technically, this chapter studies the di erent models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre-emption. In each case the operational semantics of CCS is modi ed appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for di erent process-algebraic settings are discussed.

This chapter addresses the question how to verify distributed and communicating systems in an e#ective way from an explicit process algebraic standpoint. This means that all calculations are based on the axioms and principles of the process algebras.

We present a strategy for nding algebraic correctness proofs for communication systems. It is described in the setting of CRL [11], which is, roughly, ACP [2, 3] extended with a formal treatment of the interaction between data and processes. The strategy has already been applied successfully in [4] and [10], but was not explicitly identi ed as such. Moreover, the protocols that were veri ed in these papers were rather complex, so that the general picture was obscured by the amount of details. In this paper, the proof strategy is materialised in the form of de nitions and theorems. These results reduce a large part of protocol veri cation to a number of trivial facts concerning data parameters occurring in implementation and speci cation. This greatly simpli es protocol veri cations and makes our approach amenable to mechanical assistance � experiments in this direction seem promising. The strategy is illustrated by several small examples and one larger example, the Concurrent Alternating Bit Protocol (CABP). Although simple, this protocol contains a large amount ofinternal parallelism, so that all relevant issuesmaketheir appearance.

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Jones and Plotkin give a general construction for forming a probabilistic powerdomain over any directed-complete partial order [Jon90, JP89]. We apply their technique to the failures/divergences semantic model for Communicating Sequential Processes [Hoa85]. The resulting probabilistic model supports a new binary operator, probabilistic choice, and retains all operators of CSP including its two existing forms of choice. An advantage of using the general construction is that it is easy to see which CSP identities remain true in the probabilistic model. A surprising consequence however is that probabilistic choice distributes through all other operators; such algebraic mobility means that the syntactic position of the choice operator gives little information about when the choice actually must occur. That in turn leads to some interesting interaction between probability and nondeterminism. A simple communications protocol is used to illustrate the probabilistic algebra, and several sugg...

Communicated by P.M.B. Vitiyi This note presents a detailed proof of a result in the theory of concurrency semantics that is already considered folklore, namely that branching bisimilarity is an equivalence relation. The “simple proof ‘, which in the literature is always assumed to exist, is shown to be incorrect. The proof in this note is based on the notion of a semi-branching bisimulation taken from (Van Glabbeek and Weijland, 1991). Branching bisimilarity can equivalently be defined in terms of semi-branching bisimulations; the results suggest that such a definition is more intuitive than the original definition of Van Glabbeek and Weijland ( 1989).

Abstract. We introduce mCRL2, a specification language that can be used to specify and analyse the behaviour of distributed systems. This language is the successor of the µCRL specification language. The mCRL2 language extends a timed basic process algebra with the possibility to define and use abstract data types. The mCRL2 data language features predefined and higher-order data types. The process algebraic part of mCRL2 allows a faithful translation of coloured Petri nets and component based systems: we have introduced multiactions and we have separated communication and parallelism.

Abstract. It is now well-admitted that formal methods are helpful for many issues raised in the Web service area. In this paper we present a framework for the design and verification of WSs using process algebras and their tools. We define a two-way mapping between abstract specifications written using these calculi and executable Web services written in BPEL4WS. Several choices are available: design and correct errors in BPEL4WS, using process algebra verification tools, or design and correct in process algebra and automatically obtaining the corresponding BPEL4WS code. The approaches can be combined. Process algebra are not useful only for temporal logic verification: we remark the use of simulation/bisimulation both for verification and for the hierarchical refinement design method. It is worth noting that our approach allows the use of any process algebra depending on the needs of the user at different levels (expressiveness, existence of reasoning tools, user expertise). 1

We introduce the lambda-coiteration schema for a distributive law lambda of a functor T over a functor F. Under certain conditions it can be shown to uniquely characterise functions into the carrier of a final F-coalgebra, generalising the basic coiteration schema as given by finality. The duals of primitive recursion and course-of-value iteration, which are known extensions of coiteration, arise as instances of our framework. One can furthermore obtain schemata justifying recursive specifications that involve operators such as addition of power series, regular operators on languages, or parallel and sequential composition of processes. Next...