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84
LTL with the freeze quantifier and register automata
 In LICS’06
, 2006
"... Temporal logics, firstorder logics, and automata over data words have recently attracted considerable attention. A data word is a word over a finite alphabet, together with a datum (an element of an infinite domain) at each position. Examples include timed words and XML documents. To refer to the d ..."
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Cited by 75 (7 self)
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Temporal logics, firstorder logics, and automata over data words have recently attracted considerable attention. A data word is a word over a finite alphabet, together with a datum (an element of an infinite domain) at each position. Examples include timed words and XML documents. To refer to the data, temporal logics are extended with the freeze quantifier, firstorder logics with predicates over the data domain, and automata with registers or pebbles. We investigate relative expressiveness and complexity of standard decision problems for LTL with the freeze quantifier (LTL ↓), 2variable firstorder logic (FO 2) over data words, and register automata. The only predicate available on data is equality. Previously undiscovered connections among those formalisms, and to counter automata with incrementing errors, enable us to answer several questions left open in recent literature. We show that the futuretime fragment of LTL ↓ which corresponds to FO 2 over finite data words can be extended considerably while preserving decidability, but at the expense of nonprimitive recursive complexity, and that most of further extensions are undecidable. We also prove that surprisingly, over infinite data words, LTL ↓ without the ‘until’ operator, as well as nonemptiness of oneway universal register automata, are undecidable even when there is only 1 register. 1.
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 37 (6 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.
Twovariable logic on data words
, 2007
"... In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the twovariable firstorder ..."
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Cited by 35 (4 self)
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In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the twovariable firstorder logic FO 2 (∼,<,+1) is decidable over finite and over infinite data words, where ∼ is a binary predicate testing the data value equality and +1, < are the usual successor and order predicates. The complexity of the problem is at least as hard as Petri net reachability. Several extensions of the logic are considered, some remain decidable while some are undecidable.
Alternationfree modal mucalculus for data trees
 In LICS’07
, 2007
"... An alternationfree modal µcalculus over data trees is introduced and studied. A data tree is an unranked ordered tree whose every node is labelled by a letter from a finite alphabet and an element (“datum”) from an infinite set. For expressing datasensitive properties, the calculus is equipped wi ..."
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Cited by 27 (3 self)
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An alternationfree modal µcalculus over data trees is introduced and studied. A data tree is an unranked ordered tree whose every node is labelled by a letter from a finite alphabet and an element (“datum”) from an infinite set. For expressing datasensitive properties, the calculus is equipped with freeze quantification. A freeze quantifier stores in a register the datum labelling the current tree node, which can then be accessed for equality comparisons deeper in the formula. The main results in the paper are that, for the fragment with forward modal operators and one register, satisfiability over finite data trees is decidable but not primitive recursive, and that for the subfragment consisting of safety formulae, satisfiability over countable data trees is decidable but not elementary. The proofs use alternating tree automata which have registers, and establish correspondences with nondeterministic tree automata which have faulty counters. Allowing backward modal operators or two registers causes undecidability. As consequences, decidability is obtained for two datasensitive fragments of the XPath query language. The paper shows that, for reasoning about data trees, the forward fragment of the calculus with one register is a powerful alternative to a recently proposed firstorder logic with two variables. 1.
Complexity of data tree patterns over XML documents
 in Mathematical Foundations of Computer Science (MFCS), ser. Lecture Notes in Computer Science
, 2008
"... Abstract. We consider Boolean combinations of data tree patterns as a specification and query language for XML documents. Data tree patterns are tree patterns plus variable (in)equalities which express joins between attribute values. Data tree patterns are a simple and natural formalism for expressi ..."
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Abstract. We consider Boolean combinations of data tree patterns as a specification and query language for XML documents. Data tree patterns are tree patterns plus variable (in)equalities which express joins between attribute values. Data tree patterns are a simple and natural formalism for expressing properties of XML documents. We consider first the model checking problem (query evaluation), we show that it is DPcomplete 1 in general and already NPcomplete when we consider a single pattern. We then consider the satisfiability problem in the presence of a DTD. We show that it is in general undecidable and we identify several decidable fragments. 1
Satisfiability of downward XPath with data equality tests
"... In this work we investigate the satisfiability problem for the logic XPath( ↓ ∗ , ↓, =), that includes all downward axes as well as equality and inequality tests. We address this problem in the absence of DTDs and the sibling axis. We prove that this fragment is decidable, and we nail down its comp ..."
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Cited by 22 (5 self)
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In this work we investigate the satisfiability problem for the logic XPath( ↓ ∗ , ↓, =), that includes all downward axes as well as equality and inequality tests. We address this problem in the absence of DTDs and the sibling axis. We prove that this fragment is decidable, and we nail down its complexity, showing the problem to be ExpTimecomplete. The result also holds when path expressions allow closure under the Kleene star operator. To obtain these results, we introduce a new automaton model over data trees that captures XPath( ↓ ∗ , ↓, =) and has an ExpTime emptiness problem. Furthermore, we give the exact complexity of several downwardlooking fragments.
XPath evaluation in linear time
 IN: PROC. OF PODS 2008
, 2008
"... We consider a fragment of XPath where attribute values can only be tested for equality. We show that for any fixed unary query in this fragment, the set of nodes that satisfy the query can be calculated in time linear in the document size. ..."
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Cited by 19 (1 self)
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We consider a fragment of XPath where attribute values can only be tested for equality. We show that for any fixed unary query in this fragment, the set of nodes that satisfy the query can be calculated in time linear in the document size.
Variable Automata over Infinite Alphabets
, 2010
"... Automated reasoning about systems with infinite domains requires an extension of automata, and in particular, regular automata, to infinite alphabets. Existing formalisms of such automata cope with the infiniteness of the alphabet by adding to the automaton a set of registers or pebbles, or by attri ..."
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Cited by 18 (1 self)
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Automated reasoning about systems with infinite domains requires an extension of automata, and in particular, regular automata, to infinite alphabets. Existing formalisms of such automata cope with the infiniteness of the alphabet by adding to the automaton a set of registers or pebbles, or by attributing the alphabet by labels from an auxiliary finite alphabet that is read by an intermediate transducer. These formalisms involve a complicated mechanism on top of the transition function of automata over finite alphabets and are therefore difficult to understand and to work with. We introduce and study variable finite automata over infinite alphabets (VFA). VFA form a natural and simple extension of regular (and ωregular) automata, in which the alphabet consists of letters as well as variables that range over the infinite alphabet domain. Thus, VFAs have the same structure as regular automata, only that some of the transitions are labeled by variables. We compare VFA with existing formalisms, and study their closure properties and classical decision problems. We consider the settings of both finite and infinite words. In addition, we identify and study the deterministic fragment of VFA. We show that while this fragment is sufficiently strong to express many interesting properties, it is closed under union, intersection, and complementation, and its nonemptiness and containment problems are decidable. Finally, we describe a determinization process for a determinizable subset of VFA.
Regular path queries on graphs with data
 In ICDT’12
"... Graph data models received much attention lately due to applications in social networks, semantic web, biological databases and other areas. Typical query languages for graph databases retrieve their topology, while actual data stored in them is usually queried using standard relational mechanisms. ..."
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Cited by 16 (6 self)
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Graph data models received much attention lately due to applications in social networks, semantic web, biological databases and other areas. Typical query languages for graph databases retrieve their topology, while actual data stored in them is usually queried using standard relational mechanisms. Our goal is to develop techniques that combine these two modes of querying, and give us query languages that can ask questions about both data and topology. As the basic querying mechanism we consider regular path queries, with the key difference that conditions on paths between nodes now talk not only about labels but also specify how data changes along the path. Paths that combine edge labels with data values are closely related to data words, so for stating conditions in queries, we look at several dataword formalisms developed recently. We show that many of them immediately lead to intractable data complexity for graph queries, with the notable exception of register automata, which can specify many properties of interest, and have NLOGSPACE data and PSPACE combined complexity. As register automata themselves are not easy to use in querying, we define two types of extensions of regular expressions that are more userfriendly, and develop query evaluation techniques for them. For one class, regular expressions with memory, we achieve the same bounds as for automata, and for the other class, regular expressions with equality, we also obtain tractable combined complexity of query evaluation. In addition, we show that results extends to analogs of conjunctive regular path queries.