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41
Adding nesting structure to words
 In Developments in Language Theory, LNCS 4036
, 2006
"... We propose the model of nested words for representation of data with both a linear ordering and a hierarchically nested matching of items. Examples of data with such dual linearhierarchical structure include executions of structured programs, annotated linguistic data, and HTML/XML documents. Neste ..."
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Cited by 119 (17 self)
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We propose the model of nested words for representation of data with both a linear ordering and a hierarchically nested matching of items. Examples of data with such dual linearhierarchical structure include executions of structured programs, annotated linguistic data, and HTML/XML documents. Nested words generalize both words and ordered trees, and allow both word and tree operations. We define nested word automata—finitestate acceptors for nested words, and show that the resulting class of regular languages of nested words has all the appealing theoretical properties that the classical regular word languages enjoys: deterministic nested word automata are as expressive as their nondeterministic counterparts; the class is closed under union, intersection, complementation, concatenation, Kleene*, prefixes, and language homomorphisms; membership, emptiness, language inclusion, and language equivalence are all decidable; and definability in monadic second order logic corresponds exactly to finitestate recognizability. We also consider regular languages of infinite nested words and show that the closure properties, MSOcharacterization, and decidability of decision problems carry over. The linear encodings of nested words give the class of visibly pushdown languages of words, and this class lies between balanced languages and deterministic contextfree languages. We argue that for algorithmic verification of structured programs, instead of viewing the program as a contextfree language over words, one should view it as a regular language of nested words (or equivalently, a visibly pushdown language), and this would allow model checking of many properties (such as stack inspection, prepost conditions) that are not expressible in existing specification logics. We also study the relationship between ordered trees and nested words, and the corresponding automata: while the analysis complexity of nested word automata is the same as that of classical tree automata, they combine both bottomup and topdown traversals, and enjoy expressiveness and succinctness benefits over tree automata. 1
Reasoning about XML with Temporal Logics and Automata
 In LPAR’08
"... We show that problems arising in static analysis of XML specifications and transformations can be dealt with using techniques similar to those developed for static analysis of programs. Many properties of interest in the XML context are related to navigation, and can be formulated in temporal logics ..."
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Cited by 25 (4 self)
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We show that problems arising in static analysis of XML specifications and transformations can be dealt with using techniques similar to those developed for static analysis of programs. Many properties of interest in the XML context are related to navigation, and can be formulated in temporal logics for trees. We choose a logic that admits a simple singleexponential translation into unranked tree automata, in the spirit of the classical LTLtoBüchi automata translation. Automata arising from this translation have a number of additional properties; in particular, they are convenient for reasoning about unary nodeselecting queries, which are important in the XML context. We give two applications of such reasoning: one deals with a classical XML problem of reasoning about navigation in the presence of schemas, and the other relates to verifying security properties of XML views.
Marrying words and trees
 PODS
, 2007
"... Traditionally, data that has both linear and hierarchical structure, such as annotated linguistic data, is modeled using ordered trees and queried using tree automata. In this paper, we argue that nested words and automata over nested words offer a better way to capture and process the dual structur ..."
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Cited by 24 (1 self)
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Traditionally, data that has both linear and hierarchical structure, such as annotated linguistic data, is modeled using ordered trees and queried using tree automata. In this paper, we argue that nested words and automata over nested words offer a better way to capture and process the dual structure. Nested words generalize both words and ordered trees, and allow both word and tree operations. We study various classes of automata over nested words, and show that while they enjoy expressiveness and succinctness benefits over word and tree automata, their analysis complexity and closure properties are analogous to the corresponding word and tree special cases. In particular, we show that finitestate nested word automata can be exponentially more succinct than tree automata, and pushdown nested word automata include the two incomparable classes of contextfree word languages and contextfree tree languages.
SUCCINCTNESS OF THE COMPLEMENT AND INTERSECTION OF REGULAR EXPRESSIONS
, 2008
"... We study the succinctness of the complement and intersection of regular expressions. In particular, we show that when constructing a regular expression defining the complement of a given regular expression, a double exponential size increase cannot be avoided. Similarly, when constructing a regular ..."
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Cited by 22 (5 self)
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We study the succinctness of the complement and intersection of regular expressions. In particular, we show that when constructing a regular expression defining the complement of a given regular expression, a double exponential size increase cannot be avoided. Similarly, when constructing a regular expression defining the intersection of a fixed and an arbitrary number of regular expressions, an exponential and double exponential size increase, respectively, can in worstcase not be avoided. All mentioned lower bounds improve the existing ones by one exponential and are tight in the sense that the target expression can be constructed in the corresponding time class, i.e., exponential or double exponential time. As a byproduct, we generalize a theorem by Ehrenfeucht and Zeiger stating that there is a class of DFAs which are exponentially more succinct than regular expressions, to a fixed fourletter alphabet. When the given regular expressions are oneunambiguous, as for instance required by the XML Schema specification, the complement can be computed in polynomial time whereas the bounds concerning intersection continue to hold. For the subclass of singleoccurrence regular expressions, we prove a tight exponential lower bound for intersection.
Complexity of decision problems for XML schemas and chain regular expressions
 Siam J. Comp
"... Abstract. We study the complexity of the inclusion, equivalence, and intersection problem of extended CHAin Regular Expressions (eCHAREs). These are regular expressions with a very simple structure: they basically consist of the concatenation of factors, where each factor is a disjunction of strings ..."
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Cited by 19 (8 self)
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Abstract. We study the complexity of the inclusion, equivalence, and intersection problem of extended CHAin Regular Expressions (eCHAREs). These are regular expressions with a very simple structure: they basically consist of the concatenation of factors, where each factor is a disjunction of strings, possibly extended with “∗”, “+”, or “?”. Though of a very simple from, the usage of such expressions is widespread as eCHAREs, for instance, constitute a super class of the regular expressions most frequently used in practice in schema languages for XML. In particular, we show that all our lower and upper bounds for the inclusion and equivalence problem carry over to the corresponding decision problems for extended contextfree grammars, and to singletype and restrained competition tree grammars. These grammars form abstractions of Document Type Definitions (DTDs), XML Schema definitions (XSDs) and the class of onepass preorder typeable XML schemas, respectively. For the intersection problem, we show that obtained complexities only carry over to DTDs. In this respect, we also study two other classes of regular expressions related to XML: deterministic expressions and expressions where the number of occurrences of alphabet symbols is bounded by a constant. 1. Introduction. Although
Semantics, types and effects for XML updates
 In DBPL
, 2009
"... Abstract. The W3C recently released the XQuery Update Facility 1.0, a Candidate Recommendation for an XML update language. It appears likely that this proposal will become standard. XQuery has been equipped with a formal semantics and sound type system, but there has been little work on static analy ..."
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Cited by 17 (4 self)
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Abstract. The W3C recently released the XQuery Update Facility 1.0, a Candidate Recommendation for an XML update language. It appears likely that this proposal will become standard. XQuery has been equipped with a formal semantics and sound type system, but there has been little work on static analysis or typechecking of XML updates, and the typing rules in the current W3C proposal are unsound for “transform ” queries that perform embedded updates. In this paper, we investigate the problem of schema alteration, or synthesizing an output schema describing the result of an update applied to a given input schema. We review regular expression type systems for XQuery, present a core language and semantics for W3Cstyle XML updates, and develop an effect analysis, schema alteration, and sound typing rules for updates and “transform ” queries. 1
Automata vs. logics on data words
 In CSL, volume 6247 of LNCS
, 2010
"... Abstract. The relationship between automata and logics has been investigated since the 1960s. In particular, it was shown how to determine, given an automaton, whether or not it is definable in firstorder logic with label tests and the order relation, and for firstorder logic with the successor re ..."
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Cited by 16 (3 self)
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Abstract. The relationship between automata and logics has been investigated since the 1960s. In particular, it was shown how to determine, given an automaton, whether or not it is definable in firstorder logic with label tests and the order relation, and for firstorder logic with the successor relation. In recent years, there has been much interest in languages over an infinite alphabet. Kaminski and Francez introduced a class of automata called finite memory automata (FMA), that represent a natural analog of finite state machines. A FMA can use, in addition to its control state, a (bounded) number of registers to store and compare values from the input word. The class of data languages recognized by FMA is incomparable with the class of data languages defined by firstorder formulas with the order relation and an additional binary relation for data equality. We first compare the expressive power of several variants of FMA with several data word logics. Then we consider the corresponding decision
Automata with nested pebbles capture firstorder logic with transitive closure
 LOGICAL METHODS IN COMPUTER SCIENCE VOL. 3 (2:3) 2007, PP. 1–27
, 2007
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Tree automata with global constraints
 In 12th Int. Conf. in Developments in Lang. Theory (DLT), vol. 5257 of LNCS
, 2008
"... Abstract. A tree automaton with global tree equality and disequality constraints, TAGED for short, is an automaton on trees which allows to test (dis)equalities between subtrees which may be arbitrarily faraway. In particular, it is equipped with an (dis)equality relation on states, so that whenever ..."
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Cited by 14 (0 self)
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Abstract. A tree automaton with global tree equality and disequality constraints, TAGED for short, is an automaton on trees which allows to test (dis)equalities between subtrees which may be arbitrarily faraway. In particular, it is equipped with an (dis)equality relation on states, so that whenever two subtrees t and t ′ evaluate (in an accepting run) to two states which are in the (dis)equality relation, they must be (dis)equal. We study several properties of TAGEDs, and prove decidability of emptiness of several classes. We give two applications of TAGEDs: decidability of an extension of Monadic Second Order Logic with tree isomorphism tests and of unification with membership constraints. These results significantly improve the results of [10]. 1
SchemaBased Independence Analysis for XML Updates
"... Queryupdate independence analysis is the problem of determining whether an update affects the results of a query. Queryupdate independence is useful for avoiding recomputation of materialized views and may have applications to access control and concurrency control. This paper develops static anal ..."
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Cited by 13 (2 self)
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Queryupdate independence analysis is the problem of determining whether an update affects the results of a query. Queryupdate independence is useful for avoiding recomputation of materialized views and may have applications to access control and concurrency control. This paper develops static analysis techniques for queryupdate independence problems involving core XQuery queries and updates with a snapshot semantics (based on the W3C XQuery Update Facility proposal). Our approach takes advantage of schema information, in contrast to previous work on this problem. We formalize our approach, sketch a proof of correctness, and report on the performance and accuracy of our implementation. 1.