Abstract—We give a denotational framework (a “meta model”) within which certain properties of models of computation can be compared. It describes concurrent processes in general terms as sets of possible behaviors. A process is determinate if, given the constraints imposed by the inputs, there are exactly one or exactly zero behaviors. Compositions of processes are processes with behaviors in the intersection of the behaviors of the component processes. The interaction between processes is through signals, which are collections of events. Each event is a value-tag pair, where the tags can come from a partially ordered or totally ordered set. Timed models are where the set of tags is totally ordered. Synchronous events share the same tag, and synchronous signals contain events with the same set of tags. Synchronous processes have only synchronous signals as behaviors. Strict causality (in timed tag systems) and continuity (in untimed tag systems) ensure determinacy under certain technical conditions. The framework is used to compare certain essential features of various models of computation, including Kahn process networks, dataflow, sequential processes, concurrent sequential processes with rendezvous, Petri nets, and discrete-event systems. I.

We propose a framework for the formal speci cation and veri cation of timed and hybrid systems. For timed systems we propose a speci cation language that refers to time only through age functions which measure the length of the most recent timeinterval in which agiven formula has been continuously true. We then consider hybrid systems, which are systems consisting of a non-trivial mixture of discrete and continuous components, such as a digital controller that controls acontinuous environment. The proposed framework extends the temporal logic approach which has proven useful for the formal analysis of discrete systems such as reactive programs. The new framework consists of a semantic model for hybrid time, the notion of phase transition systems, which extends the formalism of discrete transition systems, an extended version of Statecharts for the speci cation of hybrid behaviors, and an extended version of temporal logic that enables reasoning about continuous change.

Recently, significant progress has been made in the development of timed process algebras for the specification and analysis of real-time systems. This paper describes a timed process algebra called ACSR, which supports synchronous timed actions and asynchronous instantaneous events. Timed actions are used to represent the usage of resources and to model the passage of time. Events are used to capture synchronization between processes. To be able to specify real systems accurately, ACSR supports a notion of priority that can be used to arbitrate among timed actions competing for the use of resources and among events that are ready for synchronization. The paper also includes a brief overview of other timed process algebras and discusses similarities and differences between them and ACSR.

An operational semantics is defined for the language of timed CSP, in terms of two relations: an evolution relation, which describes when a process becomes another simply by allowing time to pass; and a timed transition relation, which describes when a process may become another by performing an action at a particular time. It is shown how the timed behaviours used as the basis for the denotational models of the language may be extracted from the operational semantics. Finally, the failures model for timed CSP is shown to be equivalent to may-testing, and thus to trace congruence. 1 Introduction An operational semantics for a computer programming language defines the meaning of programs written in that language in terms of how a machine is intended to execute them step by step. It therefore offers a direct intuition of how program constructs are intended to behave, in contrast with denotational approaches, which often abstract away from such considerations, and with algebraic approach...

VERSA is a tool that assists in the algebraic analysis of real-time systems. It is based on ACSR, a timed process algebra designed to express resource-bound real-time distributed systems. VERSA is designed to be both a usable and useful tool for the analysis of ACSR specifications. Usability is assured by a flexible user interface that uses ACSR's traditional notation augmented with conventions from programming languages and mathematics that allow concise specification of realistic systems. Usefulness is the result of the breadth of analysis techniques planned and currently implemented, including algebraic term rewriting and state-space exploration based techniques. 1 Introduction Reliability in real-time systems can be improved through the use of formal methods for the specification and analysis of real-time systems. Formal methods treat system components as mathematical objects and provide mathematical models to describe and predict the observable properties and behaviors of...

ABSTRACT. We extend the failures/divergences model for CSP to include a component of infinite traces. This allows us to give a denotational semantics for a version of CSP including general nondeterministic choice and infinite hiding. Unfortunately the model is an incomplete partial order, so it is by no means obvious that the necessary fixed points exist. We have two proofs of this result, one via a congruence theorem with operational semantics and one via a careful analysis of operators ' behaviour on a subset of the model. As is well known to the theoretical community, it is generally far easier to model finite nondetermJnism (where a process can only choose between finitely many options at any one time) than unbounded nondeterminism (where no such restriction applies). The difficulties encountered with unbounded nondeterminism have hitherto forced

Both pre-orders and metric spaces have been used at various times as a foundation for the solution of recursive domain equations in the area of denotational semantics. In both cases the central theorem states that a `converging' sequence of `complete' domains/spaces with `continuous' retraction pairs between them has a limit in the category of complete domains/spaces with retraction pairs as morphisms. The pre-order version was discovered first by Scott in 1969, and is referred to as Scott's inverse limit theorem. The metric version was mainly developed by de Bakker and Zucker and refined and generalized by America and Rutten. The theorem in both its versions provides the main tool for solving recursive domain equations. The proofs of the two versions of the theorem look astonishingly similar, but until now the preconditions for the pre-order and the metric versions have seemed to be fundamentally different. In this thesis we establish a more general theory of domains based on the noti...

This thesis concerns the relationship between continuous and discrete modelling paradigms for timed concurrent systems, and the exploitation of this relationship towards applications, in particular model checking. The framework we have chosen is Reed and Roscoe's process algebra Timed CSP, in which semantic issues can be examined from both a denotational and an operational perspective. The continuous-time model we use is the timed failures model; on the discrete-time side, we build a suitable model in a CSP-like setting by incorporating a distinguished tock event to model the passage of time. We study the connections between these two models and show that our framework can be used to verify certain speci cations on continuous-time processes, by building upon and extending results of Henzinger, Manna, and Pnueli's. Moreover, this veri cation can in many cases be carried out directly on the model checker FDR . Results are illustrated with a small railway level crossing case study. We also construct a second, more sophisticated discretetime model which reects continuous behaviour in a manner more consistent with one's intuition, and show that our results carry over this second model as well.

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Abstract. Timed concurrent systems are widely used in concurrent and distributed real-time software, modeling of hybrid systems, design of hardware systems (using hardware description languages), discrete-event simulation, and modeling of communication networks. They consist of concurrent components that communicate using timed signals, that is, sets of (semantically) time-stamped events. The denotational semantics of such systems is traditionally formulated in a metric space, wherein causal components are modeled as contracting functions. We show that this formulation excessively restricts the models of time that can be used. In particular, it cannot handle super-dense time, commonly used in hardware description languages and hybrid systems modeling, finite time lines, and time with no origin. Moreover, if we admit continuoustime and mixed signals (essential for hybrid systems modeling) or certain Zeno signals, then causality is no longer equivalent to its formalization in terms of contracting functions. In this paper, we offer an alternative semantic framework using a generalized ultrametric that overcomes these limitations. 1