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.

We present real time and discrete time versions of ACP with absolute timing and relative timing. The starting-point isanewrealtimeversion with absolute timing, called ACPsat, featuring urgent actions and a delay operator. The discrete time versions are conservative extensions of the discrete time versions of ACP being known as ACP dat and ACP drt. The principal version is an extension of ACP sat with integration and initial abstraction to allow for choices over an interval of time and relative timing to be expressed. Its main virtue is that it generalizes ACP without timing and most other versions of ACP with timing in a smooth and natural way. This is shown for the real time version with relative timing and the discrete time version with absolute timing.

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

In this paper we present a probabilistic extension of LOTOS which is upward compatible with LOTOS. We present testing semantics for the reactive and generative models described in [vGSST90]. While there is a certain lose of the meaning of probabilities in the reactive model, testing with probabilistic tests proves to be too strong, because it does not relate behavior expressions which we expect to be equivalent. This is why we introduce the limited generative model, where tests are not allowed to have explicit probabilities. We give a fully abstract characterization for the reactive model, while we give alternative characterizations (based on a set of essential tests) for the generative and limited generative models. We also present some algebraic laws for each of the models, including some laws which establish the difference between the three models.

This paper discusses some axioms from the literature which have been used to define properties of timed transition systems. The additivity axiom proposed by (amongst others) Wang, and Nicollin and Sifakis is compared with the trajectory axiom of Lynch and Vaandrager. Some conditions for an additive transition system to be trajectoried are discussed. These are proved sufficient by using some simple terminology from category theory to show how this problem about timed transition systems can be turned into an equivalent problem about monotone functions on partially ordered sets. We also discuss trajectory (bi)simulation, which is a variant of Ho-Stuart's path bisimulation, and use similar techniques to discuss when (bi)simulation is equivalent to trajectory (bi)simulation.

There have been significant advances on formal methods to verify complex systems recently. Nevertheless, these methods have not yet been accepted as a realistic alternative to the verification of industrial systems. One reason for this is that formal methods are still difficult to apply efficiently. Another reason is that current verification algorithms are still not efficient enough to handle many complex systems. This work addresses the problem by presenting a language designed especially to simplify writing timecritical programs. It is an imperative language with a syntax similar to C. Special constructs are provided to allow the straightforward expression of timing properties. The familiar syntax makes it easier for non-experts to use the tool. The special constructs make it possible to model the timing characteristics of the system naturally and accurately. A symbolic representation using BDDs, model checking and quantitative algorithms are used to check system timing properties.

ion The previous section treated BPA ffir with recursion modulo timed strong bisimulation. In this section the alphabet is extended with a special constant ø , to obtain BPA ffiø r with recursion, and process terms are considered modulo rooted timed branching bisimulation. In the sequel, a and ff will represent elements from A [ føg and A [ fffi; øg, respectively. 3.1 Time Shift In order to define timed branching bisimulation, the syntax is extended with the time shift operator (r)p, which takes a rational number r and a process term p. The process term (r)p denotes the behaviour of p that is shifted r units in time. Its ultimate delay is defined by U((r)p) = maxfU(p) + r; 0g The transition rules and axioms for the time shift are given in Table 4. Using axioms TS1-4, this operator can be eliminated from all process terms. 3.2 Timed Branching Bisimulation The operational semantics consists of the transition rules in Table 1 and Table 2 and Table 4. The definition of timed strong...

. Event structures are a prominent noninterleaving model for concurrency. Real-time event structures associate a set of time instants to events, modelling absolute time constraints, and to causal dependencies, modelling relative delays between causally dependent events. We introduce this novel temporal model and show how it can be used to provide a denotational semantics to a real-time variant of a process algebra akin to LOTOS. This formalism includes a timed-action prefix which constrains the occurrence time of actions, a timeout and watchdog (i.e., timed interrupt) operator. An event-based operational semantics for this formalism is presented that is shown to be consistent with the denotational semantics. As an example we use an infinite buffer with time constraints on the message latency and the rates of accepting and producing data. 1 Introduction Timed extensions of interleaving models for concurrency have been investigated thoroughly in the last decade. Although there are many...

Event structures are a prominent model for non-interleaving concurrency. The use of event structures for providing a compositional non-interleaving semantics to LOTOS without data is studied. In particular, several quantitative extensions of event structures are proposed that incorporate notions like time---both of deterministic and stochastic nature---and probability. The suitability of these models for giving a non-interleaving semantics to a timed, stochastic and probabilistic extension of LOTOS is investigated. Consistency between the event structure semantics and an (event-based) operational semantics is addressed for the different quantitative variants of LOTOS and is worked out for the timed case in more detail. These consistency results facilitate the coherent use of an interleaving and a non-interleaving semantic view in a single design trajectory and provide a justification for the event structure semantics. As a running example an infinite buffer is used in which gradually t...

Recently the use of formal methods in describing and analysing the behaviour of (computer) systems has become more common. This has resulted in the proliferation of a wide variety of different specification formalisms, together with analytical techniques and methodologies for specification development. The particular specification formalism adopted for this study is LOTOS, an ISO standard formal description technique. Although there are many works dealing with how to write LOTOS specifications and how to develop a LOTOS specification from the initial abstract requirements specification to concrete implementation, relatively few works are concerned with the problems of expressing and proving the correctness of LOTOS specifications, i.e. verification. The main objective of this thesis is to address this shortfall by investigating the meaning of verification as it relates to concurrent systems in general, and in particular to those systems described using LOTOS. Further goals are to autom...