Abstract not found

Abstract not found

In a seminal paper, McMillan proposed a technique for constructing a finite complete prefix of the unfolding of bounded (i.e., finitestate) Petri nets, which can be used for verification purposes. Contextual nets are a generalisation of Petri nets suited to model systems with readonly access to resources. When working with contextual nets, a finite complete prefix can be obtained by applying McMillan’s construction to a suitable encoding of the contextual net into an ordinary net. However, it has been observed that if the unfolding is itself a contextual net, then the complete prefix can be significantly smaller than the one obtained with the above technique. A construction for generating such a contextual complete prefix has been proposed for a special class of nets, called read-persistent. In this paper we propose an algorithm that works for arbitrary semi-weighted, bounded contextual nets. The construction explicitly takes into account the fact that, unlike in ordinary or readpersistent nets, an event can have several different histories in general contextual net computations.

Abstract. We propose a framework for model-based diagnosis of systems with mobility and variable topologies, modelled as graph transformation systems. Generally speaking, model-based diagnosis is aimed at constructing explanations of observed faulty behaviours on the basis of a given model of the system. Since the number of possible explanations may be huge we exploit the unfolding as a compact data structure to store them, along the lines of previous work dealing with Petri net models. Given a model of a system and an observation, the explanations can be constructed by unfolding the model constrained by the observation, and then removing incomplete explanations in a pruning phase. The theory is formalised in a general categorical setting: constraining the system by the observation corresponds to taking a product in the chosen category of graph grammars, so that the correctness of the procedure can be proved by using the fact that the unfolding is a right adjoint and thus it preserves products. The theory thus should be easily applicable to a wide class of system models, including graph grammars and Petri nets. 1

Abstract. Event structures have been used for giving true concurrent semantics to languages and models of concurrency such as CCS, Petri nets and graph grammars. Although certain nominal calculi have been modeled with graph grammars, and hence their event structure semantics could be obtained as instances of the general case, the main limitation is that in the case of graph grammars the construction is more complex than strictly necessary for dealing with usual nominal calculi and, speaking in categorical terms, it is not as elegant as in the case of Petri nets. The main contribution of this work is the definition of a particular class of graph grammars, called persistent, that are expressive enough to model name passing calculi while simplifying the denotational domain construction, which can be expressed as an adjunction. Finally, we apply our technique to derive event structure semantics for pi-calculus and join-calculus processes. 1

Functorial models for contextual pre-nets

Abstract: Diagnosis of concurrent and asynchronous systems, such as large telecommunication or information systems, requires powerful mathematical models. The use of Petri net unfoldings allows to formalize diagnosis using partial order semantics, a generalization from the global state model imposed by the use of automata. If, in addition to asynchronicity and distribution, the network topology itself is subject to dynamic changes, all static models, including Petri nets, reach their limits. Then, graph grammars can be used, encoding in the current local states not only the current values of state variables but also the current topology of the network connections; the fact that unfolding semantics is available allows to carry over the diagnosis algorithms to this setting.

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Graph Types" and "Updatable Graph Views".

The unfolding semantics of graph transformation systems can represent a basis for their formal veri cation. For general, possibly in nite-state, graph transformation systems one can construct nite under- and over- approximations of the (in nite) unfolding, with arbitrary accuracy. Such approximations can be used to check properties of a graph transformation system, like safety and liveness properties, expressed in suitable fragments of the -calculus. For nite-state graph transformation systems, a variant of McMillan's approach (originally developed for Petri nets) allows us to single out a nite under-approximation which is a so-called complete pre x of the unfolding, i.e., which provides an \exact" representation of the behaviour the original system as far as reachable states are concerned. Some problems related to the constructive de nition of the pre x are discussed.