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52
A Spatial Logic for Concurrency (Part I)
 Information and Computation
, 2002
"... We present a logic that can express properties of freshness, secrecy, structure, and behavior of concurrent systems. In addition to standard logical and temporal operators, our logic includes spatial operations corresponding to composition, local name restriction, and a primitive fresh name quantifi ..."
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Cited by 167 (13 self)
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We present a logic that can express properties of freshness, secrecy, structure, and behavior of concurrent systems. In addition to standard logical and temporal operators, our logic includes spatial operations corresponding to composition, local name restriction, and a primitive fresh name quantifier. Properties can also be defined by recursion
A Spatial Logic for Querying Graphs
 In Proc. of ICALP, volume 2380 of LNCS
, 2001
"... We study a spatial logic for reasoning about labelled directed graphs, and the application of this logic to provide a query language for analysing and manipulating such graphs. We give a graph description using constructs from process algebra. We introduce a spatial logic in order to reason loca ..."
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Cited by 67 (5 self)
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We study a spatial logic for reasoning about labelled directed graphs, and the application of this logic to provide a query language for analysing and manipulating such graphs. We give a graph description using constructs from process algebra. We introduce a spatial logic in order to reason locally about disjoint subgraphs. We extend our logic to provide a query language which preserves the multiset semantics of our graph model. Our approach contrasts with the more traditional setbased semantics found in query languages such as TQL, Strudel and GraphLog.
A Context Logic for Tree Update
 In Proceedings of Workshop on Logics for Resources, Processes and Programs (LRPP’04
, 2004
"... Spatial logics have been used to describe properties of treelike structures (Ambient Logic) and in a Hoare style to reason about dynamic updates of heaplike structures (Separation Logic). We integrate this work by analyzing dynamic updates to tree structures with pointers (such as XML with identif ..."
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Cited by 57 (13 self)
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Spatial logics have been used to describe properties of treelike structures (Ambient Logic) and in a Hoare style to reason about dynamic updates of heaplike structures (Separation Logic). We integrate this work by analyzing dynamic updates to tree structures with pointers (such as XML with identifiers and idrefs). Na ve adaptations of the previous logics are not expressive enough to capture such local updates. Instead we must explicitly reason about arbitrary tree contexts  not just horizontal composition and vertical branching  in order to capture updates throughout the tree. To illustrate the point, we introduce a small imperative programming language for updating our trees, small Hoarestyle axioms for the commands in the style of O'Hearn, Reynolds and Yang, and show how weakest preconditions are derivable from the small axioms with a generalized frame rule. We demonstrate the generality of our approach by showing that it collapses to Separation Logic for a heap model. 1.
Deciding Validity in a Spatial Logic for Trees
 TLDI'03
, 2003
"... We consider a propositional spatial logic for finite trees. The logic includes (tree composition), (the implication induced by composition), and 0 (the unit of composition) . We show that the satisfaction and validity problems are equivalent, and decidable. The crux of the argument is devisi ..."
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Cited by 56 (5 self)
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We consider a propositional spatial logic for finite trees. The logic includes (tree composition), (the implication induced by composition), and 0 (the unit of composition) . We show that the satisfaction and validity problems are equivalent, and decidable. The crux of the argument is devising a finite enumeration of trees to consider when deciding whether a spatial implication is satisfied. We introduce a sequent calculus for the logic, and show it to be sound and complete with respect to an interpretation in terms of satisfaction. Finally, we describe a complete proof procedure for the sequent calculus. We envisage applications in the area of logicbased type systems for semistructured data. We describe a small programming language based on this idea.
Counting in Trees for Free
, 2004
"... In [22], it was shown that MSO logic for ordered unranked trees becomes undecidable if Presburger constraints are allowed at children of nodes. We now show that a decidable logic is obtained if we use a a modal fixpoint logic instead. We present an automata theoretic characterization of this logi ..."
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Cited by 48 (2 self)
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In [22], it was shown that MSO logic for ordered unranked trees becomes undecidable if Presburger constraints are allowed at children of nodes. We now show that a decidable logic is obtained if we use a a modal fixpoint logic instead. We present an automata theoretic characterization of this logic by means of deterministic Presburger tree automata (PTA) and show how it can be used to express numerical document queries. Surprisingly, the complexity of satisfiability for the extended logic is asymptotically the same as for the original logic. The nonemptiness for PTAs is in general pspacecomplete which is moderate given that it is already pspacehard to test whether the complement of a regular expression is nonempty. We also identify a subclass of PTAs with a tractable nonemptiness problem. Further, to decide whether a tree t satisfies a formula # is polynomial in the size of # and linear in the size of t.
The decidability of model checking mobile ambients
 In Proceedings of the 15th Annual Conference of the European Association for Computer Science Logic, volume 2142 of LNCS
, 2001
"... We settle the complexity bounds of the model checking problem for the ambient calculus with public names against the ambient logic. We show that if either the calculus contains replication or the logic contains the guarantee operator, the problem is undecidable. In the case of the replicationfree c ..."
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Cited by 43 (5 self)
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We settle the complexity bounds of the model checking problem for the ambient calculus with public names against the ambient logic. We show that if either the calculus contains replication or the logic contains the guarantee operator, the problem is undecidable. In the case of the replicationfree calculus and guaranteefree logic we prove that the problem is PSPACEcomplete. For the complexity upperbound, we devise a new representation of processes that remains of polynomial size during process execution; this allows us to keep the model checking procedure in polynomial space. Moreover, we prove PSPACEhardness of the problem for several quite simple fragments of the calculus and the logic; this suggests that there are no interesting fragments with polynomialtime model checking algorithms.
LOGICS FOR UNRANKED TREES: AN OVERVIEW
 CONSIDERED FOR PUBLICATION IN LOGICAL METHODS IN COMPUTER SCIENCE
, 2006
"... Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to ..."
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Cited by 40 (7 self)
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Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to relate complex properties of trees to the existence of tree automata for those properties. Furthermore, logics differ significantly in their modelchecking properties, their automata models, and their behavior on ordered and unordered trees. In this paper we present a survey of logics for unranked trees.
Numerical document queries
 PODS
, 2003
"... A query against a database behind a site like Napster may search, e.g., for all users who have downloaded more jazz titles than pop music titles. In order to express such queries, we extend classical monadic secondorder logic by Presburger predicates which pose numerical restrictions on the childre ..."
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Cited by 39 (3 self)
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A query against a database behind a site like Napster may search, e.g., for all users who have downloaded more jazz titles than pop music titles. In order to express such queries, we extend classical monadic secondorder logic by Presburger predicates which pose numerical restrictions on the children (content) of an element node and provide a precise automatatheoretic characterization. While the existential fragment of the resulting logic is decidable, it turns out that satisfiability of the full logic is undecidable. Decidable satisfiability and a querying algorithm even with linear data complexity can be obtained if numerical constraints are only applied to those contents of elements where ordering is irrelevant. Finally, it is sketched how these techniques can be extended also to answer questions like, e.g., whether the total price of the jazz music downloaded so far exceeds a user’s budget.
Manipulating Trees with Hidden Labels
, 2003
"... We define an operational semantics and a type system for manipulating semistructured data that contains hidden information. The data model is simple labeled trees with a hiding operator. Data manipulation is based on pattern matching, with types that track the use of hidden labels. ..."
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Cited by 34 (4 self)
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We define an operational semantics and a type system for manipulating semistructured data that contains hidden information. The data model is simple labeled trees with a hiding operator. Data manipulation is based on pattern matching, with types that track the use of hidden labels.