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45
Satisfiability of a spatial logic with tree variables
 In Proc. 21st Int. Workshop on Computer Science Logic (CSL
, 2007
"... 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 ..."
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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 XMLoriented tasks, we investigate the guarded TQL fragment. We prove that for closed formulas this fragment is MSOcomplete. 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
When Ambients Cannot be Opened
 In Proceedings of FoSSaCS 2003
, 2003
"... 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 reduct ..."
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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 nameconvergence problem as well as the modelchecking problem turn out to be undecidable for both the original and the weaker reduction relation. 1
Decidability of Freshness, Undecidability of Revelation
 IN PROC. OF INTERNATIONAL CONFERENCE ON FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATIONAL STRUCTURES (FOSSACS), VOLUME 2987 OF LNCS
, 2003
"... We study decidability of a logic for describing processes with restricted names. We choose a minimal fragment of the Ambient Logic, but the techniques we present should apply to every logic which uses Cardelli and Gordon revelation and hiding operators, and Gabbay and Pitts freshness quantifier. We ..."
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We study decidability of a logic for describing processes with restricted names. We choose a minimal fragment of the Ambient Logic, but the techniques we present should apply to every logic which uses Cardelli and Gordon revelation and hiding operators, and Gabbay and Pitts freshness quantifier. We start from the static fragment of ambient logic that Calcagno Cardelli and Gordon proved to be decidable. We prove that the addition of a hiding quantifier makes the logic undecidable. Hiding can be decomposed as freshness plus revelation. Quite surprisingly, freshness alone is decidable, but revelation alone is not.
Adjuncts elimination in the static ambient logic
, 2003
"... The Ambient Logic (AL) has been proposed for expressing spatial properties of processes of the Mobile Ambient calculus (MA). Restricting both the calculus and the logic to their static part yields static ambients (SA) and the static ambient logic (SAL), that form a model for queries about semistruct ..."
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Cited by 9 (2 self)
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The Ambient Logic (AL) has been proposed for expressing spatial properties of processes of the Mobile Ambient calculus (MA). Restricting both the calculus and the logic to their static part yields static ambients (SA) and the static ambient logic (SAL), that form a model for queries about semistructured data. SAL also includes the nonstandard fresh quantifier (I). This work adresses the questions of expressiveness and minimality of SAL from the point of view of adjuncts. We define the intensional fragment of the logic (SALint), the logic without adjuncts, and prove that it captures all the expressiveness of the logic. We moreover study the question of adjuncts elimination in SAL ∀ , where I quantifier is replaced by the classical ∀ quantifier. We conclude with a proof of the minimality of SALint.
Elimination of spatial connectives in static spatial logics
, 2003
"... The recent interest for specification on resources yields socalled 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 (− ∗ , ..."
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Cited by 9 (0 self)
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The recent interest for specification on resources yields socalled 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.
Elimination of Quantifiers and Undecidability in Spatial Logics for Concurrency
, 2004
"... 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 ..."
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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 quantifierfree. Finally, we prove that both modelchecking 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.
Model Checking for Combined Logics with an Application to Mobile Systems
 AUTOMATED SOFTWARE ENGINEERING
, 2004
"... 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 ..."
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Cited by 8 (1 self)
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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.
A Complete Axiomatic System for Processbased Spatial Logic
 In Proc. of MFCS 2008, LNCS 5168
, 2008
"... Abstract. The processbased Spatial Logics are multimodal logics developed for semantics on Process Algebras and designed to specify concurrent properties of dynamic systems. On the syntactic level, they combine modal operators similar to operators of HennessyMilner logic, dynamic logic, arrow l ..."
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Abstract. The processbased Spatial Logics are multimodal logics developed for semantics on Process Algebras and designed to specify concurrent properties of dynamic systems. On the syntactic level, they combine modal operators similar to operators of HennessyMilner logic, dynamic logic, arrow logic, relevant logic, or linear logic. This combination generates expressive logics, sometimes undecidable, for which a wide range of applications have been proposed. In the literature, there exist some sound proof systems for spatial logics, but the problem of completeness against processalgebraic semantics is still open. The main goal of this paper is to identify a soundcomplete axiomatization for such a logic. We focus on a particular spatial logic that combines the basic spatial operators with dynamic and classical operators. The semantics is based on a fragment of CCS calculus that embodies the core features of concurrent behaviors. We prove the logic decidable both for satisfiability/validity and modechecking, and we propose a soundcomplete Hilbertstyle axiomatic system for it. 1
Nesting analysis of mobile ambients
, 2004
"... A new algorithm is introduced for analyzing possible nestings in mobile ambient calculus. It improves both time and space complexities of the technique proposed by Nielson and Seidl. The improvements are achieved by enhancing the data structure representations, and by reducing the computation to the ..."
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Cited by 4 (1 self)
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A new algorithm is introduced for analyzing possible nestings in mobile ambient calculus. It improves both time and space complexities of the technique proposed by Nielson and Seidl. The improvements are achieved by enhancing the data structure representations, and by reducing the computation to the control ow analysis constraints that are effectively necessary to get to the least solution. These theoretical results are also supported by experimental tests run on a Javabased tool that implements a suite of algorithms for nesting analysis of mobile ambients.