We investigate expressiveness of a fragment of the ambient calculus, a formalism for describing distributed and mobile computations. More precisely, we study expressiveness of the pure and public ambient calculus from which the has been removed, in terms of the reachability problem of the reduction relation. Surprisingly, we show that even for this very restricted fragment, the reachability problem is not decidable. At a second step, for a slightly weaker reduction relation, we prove that reachability can be decided by reducing this problem to markings reachability for Petri nets. Finally, we show that the name-convergence problem as well as the model-checking problem turn out to be undecidable for both the original and the weaker reduction relation. 1

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The introduction of spatial logics in concurrency is motivated by a shift of focus from concurrent systems towards distributed systems. Aiming at a deeper understanding of the essence of dynamic spatial logics, we study a minimal spatial logic without quantifiers or any operators talking about names. The logic just includes the basic spatial operators void, composition and its adjunct, and the next step modality; for the model we consider a tiny fragment of CCS. We show that this core logic can already encode its own extension with quantifiers, and modalities for actions. From this result, we derive several consequences. Firstly, we establish the intensionality of the logic, we characterize the equivalence it induces on processes, and we derive characteristic formulas. Secondly, we show that, unlike in static spatial logics, the composition adjunct adds to the expressiveness of the logic, so that adjunct elimination is not possible for dynamic spatial logics, even quantifier-free. Finally, we prove that both model-checking and satisfiability problems are undecidable in our logic. We also conclude that our results extend to other calculi, namely the #-calculus and the ambient calculus.

The recent interest for specification on resources yields so-called spatial logics, that is specification languages offering spatial connectives: a separation into two subcomponents of the considered structure, (∗,or |), and its adjunct, the guarantee respect to the extension of the structure (− ∗ , ⊲). We consider two resource models and their related logics: • the Static Ambient (SA), proposed as a model of semistructured data [4], with the Static Ambient Logic (SAL) that was proposed as a request language, both obtained restricting the Mobile Ambient calculus [5] and logic [6] to their purely static aspects. • the shared mutable data structures adressed by the Separation Logic (SL), as it has been defined in [15] as an adequate assertion language for Hoare style reasoning on imperative programs manipulating pointers. We raise the questions of the expressiveness and the minimality of these logics. Our main contributions are the elimination of adjuncts for SAL, the minimality of the adjunctfree fragment (SALint), and the elimination of both spatial connectives ∗ and − ∗ for SL.

Abstract. We investigate in this paper the spatial logic TQL for querying semistructured data, represented as unranked ordered trees over an infinite alphabet. This logic consists of usual Boolean connectives, spatial connectives (derived from the constructors of a tree algebra), tree variables and a fixpoint operator for recursion. Motivated by XML-oriented tasks, we investigate the guarded TQL fragment. We prove that for closed formulas this fragment is MSO-complete. In presence of tree variables, this fragment is strictly more expressive than MSO as it allows for tree (dis)equality tests, i.e. testing whether two subtrees are isomorphic or not. We devise a new class of tree automata, called TAGED, which extends tree automata with global equality and disequality constraints. We show that the satisfiability problem for guarded TQL formulas reduces to emptiness of TAGED. Then, we focus on bounded TQL formulas: intuitively, a formula is bounded if for any tree, the number of its positions where a subtree is captured by a variable is bounded. We prove this fragment to correspond with a subclass of TAGED, called bounded TAGED, for which we prove emptiness to be decidable. This implies the decidability of the bounded guarded TQL fragment. Finally, we compare bounded TAGED to a fragment of MSO extended with subtree isomorphism tests. 1

In this paper, we develop model checking procedures for three ways of combining (temporal) logics: temporalization, independent combination, and join. We prove that they are terminating, sound, and complete, we analyze their computational complexity, and we report on experiments with implementations. We take a close look at mobile systems and show how the proposed combined model checking framework can be successfully applied to the specification and verification of their properties.

The Brane Calculus is a calculus of mobile processes, intended to model the transport machinery of a cell system. In this paper, we introduce the Brane Logic, a modal logic for expressing formally properties about systems in Brane Calculus. Similarly to previous logics for mobile ambients, Brane Logic has specific spatial and temporal modalities. Moreover, since in Brane Calculus the activity resides on membrane surfaces and not inside membranes, we need to add a specific logic (akin Hennessy-Milner’s) for reasoning about membrane activity. We present also a proof system for deriving valid sequents in Brane Logic. Finally, we present a model checker for a decidable fragment of this logic.

We propose a new class of logics for specifying and model-checking properties of distributed systems- Dynamic Epistemic Spatial Logics. They have been designed as extensions of Hennessy-Milner logic with spatial operators (inspired by Cardelli-Caires spatial logic) and epistemic operators (inspired by dynamic-epistemic logics). Our logics focus on observers, agents placed in different locations of the system having access to some subsystems. Treating them as epistemic agents, we develop completely axiomatized and decidable logics that express the information flow between them in a dynamic and distributed environment. The knowledge of an epistemic agent, is understood as the information, locally available to our observer, about the overall-global system. By combining the knowledge of different observers we can specify properties of the whole system. Dynamic Epistemic Spatial Logics are decidable against a semantics based on a fragment of CCS for which the classical spatial logics have been proved to be undecidable. Eventually model-checking and satisfiability/validity-checking algorithms are presented. 1

A new algorithm is introduced for analysing possible nesting in Mobile Ambients calculus.

The field of pervasive computing has seen a lot of exciting innovations in the past few years. However, there are currently no mechanisms for describing the properties and capabilities of pervasive computing environments in a formal manner. This makes it difficult to prove the correctnesss of a pervasive computing environment, i.e. to verify that the environment satisfies certain desired properties. In this paper, we propose a formal model for describing pervasive computing environments based on ambient calculus and the associated ambient logic. The model allows us to state and verify several properties of these environments such as “anywhere anyhow services”, “mobility of devices and applications ” and “context-aware adaptation”. The model allows us to describe the resources present in an environment, the operations that can be performed in the environment, and how users can use the resources in th environment to perform different kinds of activities. As a case study, we shall describe some of the resources and operations supported by the Gaia middleware using this model, and verify an example property of a pervasive computing environment supported by Gaia. 1