We study a process algebra ATP for the description and analysis of systems of timed processes. An important feature of the algebra is that its vocabulary of actions contains a distinguished element . An occurrence of is a time event representing progress of time. The algebra has, apart from standard operators of process algebras like CCS or ACP, a primitive binary unit-delay operator. For two arguments, processes P and Q, this operator gives a process which behaves as P if started before the occurrence of a time action and as Q otherwise. From this operator we define d-unit delay operators that can model delay constructs of languages, like timeouts or watchdogs. The use of such operators is illustrated by examples. ATP is provided with a complete axiomatisation with respect to strong bisimulation semantics. It is shown that the algebras obtained by adding the various d-unit delay operators to ATP are conservative extensions of it.

Abstract The Concurrency Workbench is an automated tool for analyzing networks of finite-state processes expressed in Milner's Calculus of Communicating Systems. Its key feature is its breadth: a variety of different verification methods, including equivalence checking, preorder checking, and model checking, are supported for several different process semantics. One experience from our work is that a large number of interesting verification methods can be formulated as combinations of a small number of primitive algorithms. The Workbench has been applied to the verification of communications protocols and mutual exclusion algorithms and has proven a valuable aid in teaching and research. 1 Introduction This paper describes the Concurrency Workbench [11, 12, 13], a tool that supports the automatic verification of finite-state processes. Such tools are practically motivated: the development of complex distributed computer systems requires sophisticated verification techniques to guarantee correctness, and the increase in detail rapidly becomes unmanageable without computer assistance. Finite-state systems, such as communications protocols and hardware, are particularly suitable for automated analysis because their finitary nature ensures the existence of decision procedures for a wide range of system properties.

We extend Milner's SCCS to obtain a calculus, PCCS, for reasoning about communicating probabilistic processes. In particular, the nondeterministic process summation operator of SCCS is replaced with a probabilistic one, in which the probability of behaving like a particular summand is given explicitly. The operational semantics for PCCS is based on the notion of probabilistic derivation, and is given structurally as a set of inference rules. We then present an equational theory for PCCS based on probabilistic bisimulation, an extension of Milner's bisimulation proposed by Larsen and Skou. We provide the first axiomatization of probabilistic bisimulation, a subset of which is relatively complete for finite-state probabilistic processes. In the probabilistic case, a notion of processes with almost identical behavior (i.e., with probability 1 \Gamma ffl, for ffl sufficiently small) appears to be more useful in practice than a notion of equivalence, since the latter is often too restricti...

this paper have been presented at the 4th European Summer School in Logic, Language and Information, University of Essex, 1992; at the Tempus Summer School for Algebraic and Categorical Methods in Computer Science, Masaryk University, Brno, 1993; and the Summer School in Logic Methods in Concurrency, Aarhus University, 1993. I would like to thank the organisers and the participants of these summer schools, and of the Banff higher order workshop. I would also like to thank Julian Bradfield for use of his Tex tree constructor for building derivation trees and Carron Kirkwood, Faron Moller, Perdita Stevens and David Walker for comments on earlier drafts.

A simple efficiency preorder for CCS processes is introduced, in which p ! q means that q is at least as fast as p, or more generally, p uses at least as much resources as q. It is shown to be preserved by all CCS contexts except summation and it is used to analyse a non-trivial example: different implementations of a bounded buffer. Finally a sound and complete proof system for finite processes is given. This paper appeared earlier in [1] and [2]. This version of the paper has been revised, corrected and extended to include more operators, more examples and some additional remarks and observations by the first author. Hence all errors are entirely his responsiblity. Most of this work was done while the first author was at the University of Sussex and supported by SERC grant GR/D 97368 of the Science and Engineering Research Council of Great Britain. y The second author would like to acknowledge the support of ESPIRIT II. 1 Introduction A large number of behavioural equivale...

CBS is a simple and natural CCS-like calculus where processes speak one at a time and are heard instantaneously by all others. Speech is autonomous, contention between speakers being resolved nondeterministically, but hearing only happens when someone else speaks. Observationally meaningful laws differ from those of CCS. The change from handshake communication in CCS to broadcast in CBS permits several advances. (1) Priority, which attaches only to autonomous actions, is simply added to CBS in contrast to CCS, where such actions are the result of communication. (2) A CBS simulator runs a process by returning a list of values it broadcasts. This permits a powerful combination, CBS with the host language. It yields several elegant algorithms. Only processes with a unique response to each input are needed in practice, so weak bisimulation is a congruence. (3) CBS subsystems are interfaced by translators; by mapping messages to silence, these can restrict hearing and hide speech. Reversi...

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. EMPA enhances the expressiveness of classical process algebras by integrating functional and performance descriptions of concurrent systems. This is achieved by offering, besides passive actions (useful for pure nondeterminism), actions whose duration is exponentially distributed as well as immediate actions (useful for performance abstraction), parametrized by priority levels (hence prioritized choices) and weights (hence probabilistic choices). In order to analyze an EMPA term, from its integrated semantic model (a transition system labeled on both action types and action durations) we derive a functional semantic model (a transition system labeled on action types only) and a performance semantic model (a Markov chain). We show that an integrated analysis, i.e. a notion of equivalence on the integrated semantic model, is not only convenient but also necessary to achieve compositionality. 1 Introduction The need of integrating the performance modeling and analysis of a concurrent s...

Abstract. We study causality in the ß-calculus. Our notion of causality combines the dependencies given by the syntactic structure of processes with those originated by passing names. It turns out that two transitions not causally related may although occur in a fixed ordering in any computation, i.e., ß-calculus may express implicitly a priority between actions. Our causality relation still induces the same partial order of transitions for all the computations that are obtained by shuffling transitions that are concurrent (= related neither by causality nor by priority). The presentation takes advantage from a parametric definition of process behaviour that highlights the essence of the topic. All the results on bisimulation based equivalences, congruences, axiomatizations and logics are taken (almost) for free from the interleaving theory. 1 Introduction The study of the behaviour of a distributed system may benefit from knowledge on the causal relation between its events. For examp...

Statecharts is a visual language for specifying reactive system behavior. The formalism extends traditional finite-state machines with notions of hierarchy and concurrency, and it is used in many popular software design notations. A large part of the appeal of Statecharts derives from its basis in state machines, with their intuitive operational interpretation. The traditional semantics of Statecharts, however, suffers from a serious defect: it is not compositional, meaning that the behavior of system descriptions cannot be inferred from the behavior of their subsystems. Compositionality is a prerequisite for exploiting the modular structure of Statecharts for simulation, verification, and code generation, and it also provides the necessary foundation for reusability. This paper suggests a new compositional approach to formalizing Statecharts semantics as flattened transition systems in which transitions represent system steps. The approach builds on ideas developed for timed process ca...