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23
Querying unranked trees with stepwise tree automata
 Intenational Conf. on Rewriting Techniques and Applications
, 2004
"... Abstract. The problem of selecting nodes in unranked trees is the most basic querying problem for XML. We propose stepwise tree automata for querying unranked trees. Stepwise tree automata can express the same monadic queries as monadic Datalog and monadic secondorder logic. We prove this result by ..."
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Cited by 43 (20 self)
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Abstract. The problem of selecting nodes in unranked trees is the most basic querying problem for XML. We propose stepwise tree automata for querying unranked trees. Stepwise tree automata can express the same monadic queries as monadic Datalog and monadic secondorder logic. We prove this result by reduction to the ranked case, via a new systematic correspondence that relates unranked and ranked queries. 1
A Logic You Can Count On
 In POPL 2004 – 31st Annual ACM SIGPLANSIGACT Symposium on Principles of Programming Languages
, 2004
"... We prove the decidability of the quantifierfree, static fragment of ambient logic, with composition adjunct and iteration, which corresponds to a kind of regular expression language for semistructured data. The essence of this result is a surprising connection between formulas of the ambient logic ..."
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Cited by 21 (0 self)
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We prove the decidability of the quantifierfree, static fragment of ambient logic, with composition adjunct and iteration, which corresponds to a kind of regular expression language for semistructured data. The essence of this result is a surprising connection between formulas of the ambient logic and counting constraints on (nested) vectors of integers.
Efficient inclusion checking for deterministic tree automata and xml schemas
, 2007
"... Abstract. We present a new algorithm for testing language inclusion L(A) ⊆ L(B) between tree automata in time O(A  ∗ B) where B is deterministic. We extend this algorithm for testing inclusion between automata for unranked trees A and deterministic DTDs D in time O(A∗ Σ  ∗ D). No previo ..."
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Cited by 17 (7 self)
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Abstract. We present a new algorithm for testing language inclusion L(A) ⊆ L(B) between tree automata in time O(A  ∗ B) where B is deterministic. We extend this algorithm for testing inclusion between automata for unranked trees A and deterministic DTDs D in time O(A∗ Σ  ∗ D). No previous algorithms with these complexities exist. inria00192329, version 6 5 Mar 2009 1
Expressiveness of a spatial logic for trees
 In Proc. IEEE Symp. on Logic in Comp. Sci
, 2005
"... In this paper we investigate the quantifierfree fragment of the TQL logic proposed by Cardelli and Ghelli. The TQL logic, inspired from the ambient logic, is the core of a query language for semistructured data represented as unranked and unordered trees. The fragment we consider here, named STL, c ..."
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Cited by 14 (4 self)
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In this paper we investigate the quantifierfree fragment of the TQL logic proposed by Cardelli and Ghelli. The TQL logic, inspired from the ambient logic, is the core of a query language for semistructured data represented as unranked and unordered trees. The fragment we consider here, named STL, contains as main features spatial composition and location as well as a fixed point construct. We prove that satisfiability for STL is undecidable. We show also that STL is strictly more expressive than the Presburger monadic secondorder logic (PMSO) of Seidl, Schwentick and Muscholl when interpreted over unranked and unordered edgelabelled trees. We define a class of tree automata whose transitions are conditioned by arithmetical constraints; we show then how to compute from a closed STL formula a tree automaton accepting precisely the models of the formula. Finally, still using our tree automata framework, we exhibit some syntactic restrictions over STL formulae that allow us to capture precisely the logics MSO and PMSO. 1
Typed iterators for XML
, 2007
"... XML transformations are very sensitive to types: XML types describe the tags and attributes of XML elements as well as the number, kind, and order of their subelements. Therefore, even very basic operations such as changing a tag, renaming an attribute, or adding an element generally imply conspicu ..."
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Cited by 12 (1 self)
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XML transformations are very sensitive to types: XML types describe the tags and attributes of XML elements as well as the number, kind, and order of their subelements. Therefore, even very basic operations such as changing a tag, renaming an attribute, or adding an element generally imply conspicuous changes from the type of the input to the type of the output. Such operations are applied on XML documents by iterators that, to be useful, need to be typed by some kind of polymorphism that goes beyond what currently exists. For this reason these iterators are not programmed but, rather, hardcoded in the language. However, this approach soon reaches its limits, as the hardcoded iterators cannot cover fairly standard usage scenarios. As a solution to this problem we propose a generic language to define iterators for XML data to be grafted on some host programming language. We show that our language mostly offers the required degree of polymorphism, study its formal properties, and show its expressiveness and practical impact by providing several usage examples and encodings.
Counting in trees
, 2007
"... We consider automata and logics that allow to reason about numerical properties of unranked trees, expressed as Presburger constraints. We characterize nondeterministic automata by Presburger Monadic SecondOrder logic, and deterministic automata by Presburger Fixpoint logic. We show how our resul ..."
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Cited by 9 (0 self)
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We consider automata and logics that allow to reason about numerical properties of unranked trees, expressed as Presburger constraints. We characterize nondeterministic automata by Presburger Monadic SecondOrder logic, and deterministic automata by Presburger Fixpoint logic. We show how our results can be used in order to obtain efficient querying algorithms on XML trees.
Unranked tree automata with sibling equalities and disequalities
, 2006
"... We propose an extension of the tree automata with constraints between direct subtrees (Bogaert and Tison, 1992) to unranked trees. Our approach uses MSOformulas to capture the possibility of comparing unboundedly many direct subtrees. Our main result is that the nonemptiness problem for the deter ..."
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Cited by 9 (1 self)
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We propose an extension of the tree automata with constraints between direct subtrees (Bogaert and Tison, 1992) to unranked trees. Our approach uses MSOformulas to capture the possibility of comparing unboundedly many direct subtrees. Our main result is that the nonemptiness problem for the deterministic automata, as in the ranked setting, is decidable. It turns out that the main difficulty is indeed the absence of the rank, as it gives a certain bound on the number of distinct subtrees needed in order to satisfy an equality or disequality constraint. We overcome this difficulty by finding such a bound via a bruteforce method.
Presburger modal logic is PSPACEcomplete
, 2006
"... Abstract. We introduce a Presburger modal logic PML with regularity constraints and full Presburger constraints on the number of children that generalize graded modalities, also known as number restrictions in description logics. We show that PML satisfiability is only pspacecomplete by designing a ..."
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Cited by 4 (0 self)
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Abstract. We introduce a Presburger modal logic PML with regularity constraints and full Presburger constraints on the number of children that generalize graded modalities, also known as number restrictions in description logics. We show that PML satisfiability is only pspacecomplete by designing a Ladnerlike algorithm. This extends a wellknown and nontrivial pspace upper bound for graded modal logic. Furthermore, we provide a detailed comparison with logics that contain Presburger constraints and that are dedicated to query XML documents. As an application, we show that satisfiability for Sheaves Logic SL is pspacecomplete, improving significantly its best known upper bound. 1
Adding monotonic counters to automata and transition graphs
 Proc. 9th Conf. on Developments in Language Theory, Springer LNCS 3572
, 2005
"... Abstract. We analyze models of infinitestate automata extended by monotonic counting mechanisms, starting from the (finitestate) Parikh automata studied by Klaedtke and Rueß. We show that, for linearbounded automata, this extension does not increase the language recognition power. In the framework ..."
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Cited by 2 (0 self)
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Abstract. We analyze models of infinitestate automata extended by monotonic counting mechanisms, starting from the (finitestate) Parikh automata studied by Klaedtke and Rueß. We show that, for linearbounded automata, this extension does not increase the language recognition power. In the framework of infinite transition systems developed by Caucal and others, we show that adding monotonic counters to synchronized rational graphs still results in synchronized rational graphs, in contrast to the case of pushdown graphs or prefixrecognizable graphs. For prefixrecognizable graphs, however, we show that the extension by monotonic counters retains the decidability of the reachability problem. 1