this paper various semantics in the linear time -- branching time spectrum are presented in a uniform, model-independent way. Restricted to the class of finitely branching, concrete, sequential processes, only fifteen of them turn out to be different, and most semantics found in the literature that can be defined uniformly in terms of action relations coincide with one of these fifteen. Several testing scenarios, motivating these semantics, are presented, phrased in terms of `button pushing experiments' on generative and reactive machines. Finally twelve of these semantics are applied to a simple language for finite, concrete, sequential, nondeterministic processes, and for each of them a complete axiomatization is provided.

Prefix iteration is a variation on the original binary version of the Kleene star operation P Q, obtained by restricting the first argument to be an atomic action. The

The aim of this paper is to nd the nest `observable ' and `implementable' equivalence on concurrent processes. This is a part of a larger programme to develop a theory of observable processes where semantics of processes are based on locally and nitely observable process behaviour, and all process constructs are allowed, provided their operational meaning is de ned by realistically implementable transition rules.

This paper is concerned with bisimulation relations which do not only require related agents to simulate each others behavior in the direction of the arrows, but also to simulate each other when going back in history. First it is demonstrated that the back and forth variant of strong bisimulation leads to the same equivalence as the ordinary notion of strong bisimulation. Then it is shown that the back and forth variant of Milner's observation equivalence is different from (and finer than) observation equivalence. In fact we prove that it coincides with the branching bisimulation equivalence of Van Glabbeek & Weijland. Also the back and forth variants of branching, ~ and delay bisimulation lead to branching bisimulation equivalence. The notion of back and forth bisimulation moreover leads to characterizations of branching bisimulation in terms of abstraction homomorphisms and in terms of Hencessy-Milner logic with backward modalities. In our view these results support the claim that branching bisimulation is a natural and important notion. The notion of bisimulation relation has been introduced by PARK [18]. It leads to an equivalence on labelled transition systems which, in case image finiteness is assumed, coincides with the strong equivalence of ~IILNER [12]. The great importance and usefulness of bisimulalions

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We present a general and uniform method for defining structural operational semantics (SOS) of process algebra operators by traditional Plotkin-style rules equipped with an ordering, the new feature which states the order of application of rules when deriving transitions of process terms. Our method allows to represent negative premises and copying in the presence of silent actions. We identify a number of general formats of unordered and ordered rules with silent actions and show that divergence sensitive branching and weak bisimulation relations are preserved by all operators in the relevant formats. A comparison with the existing formats for branching and weak bisimulations shows that our formats are more general.

We prove that testing preorder of De Nicola and Hennessy is preserved by all operators of De Simone process languages. Building upon this result we propose an algorithm for generating axiomatisations of testing preorder for arbitrary De Simone process languages. The axiom systems produced by our algorithm are finite and complete for processes with nite behaviour. In order to achieve completeness for a subclass of processes with infiite behaviour we use one infinitary induction rule. The usefulness of our results is illustrated in specification and verification of small concurrent systems, where suspension, resumption and alternation of execution of component systems occur. We argue that better speci cations can be written in customised De Simone process languages, which contain both the standard operators as well as new De Simone operators that are specifically tailored for the task in hand. Moreover, the automatically generated axiom systems for such specification languages make the verification more straightforward.

. We present a dynamic form of observational logic for specifying concurrent systems on the basis of their observable behaviour, in particular without needing a language for describing states, which are regarded as non-observable. The logic is based on quantales. The models are labelled transition systems, and a weakly complete proof system is presented. We study the logic from the point of view of modularity; vertical modularity is based on a notion of implementation of systems and refinement of specifications, and horizontal modularity is based on parallel composition of systems and specifications. Several compositionality results are presented. As an example we see a specification of a stack and its implementation over an array and a pointer. 1 Introduction This paper introduces a logic for specifying concurrent systems on the basis of their observable behaviour, in particular without needing a language for describing states, which are regarded as non-observable and ultimately phys...

In this paper, we present a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the GSOS format of Bloom, Istrail and Meyer. The canonical model used for this purpose will be Abramsky's domain of synchronization trees, and the denotational semantics automatically generated by our methods will be guaranteed to be fully abstract with respect to the finitely observable part of the bisimulation preorder. In the process of establishing the full abstraction result, we also obtain several general results on the bisimulation preorder (including a complete axiomatization for it), and give a novel operational interpretation of GSOS languages.

this paper has generated a veritable industry of results on the meta-theory of SOS and process algebras. (See [10] for a mention of some of these achievements and pointers to the original literature.) The proof techniques used in these results were extremely ingenious, and have paved the way to many similar developments. Again, the role played by the modal characterizations of behavioural equivalences in the proof of the characterizations of the largest congruences is remarkable