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Visibly pushdown languages
, 2004
"... Abstract. We study congruences on words in order to characterize the class of visibly pushdown languages (Vpl), a subclass of contextfree languages. For any language L, we define a natural congruence on words that resembles the syntactic congruence for regular languages, such that this congruence i ..."
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Abstract. We study congruences on words in order to characterize the class of visibly pushdown languages (Vpl), a subclass of contextfree languages. For any language L, we define a natural congruence on words that resembles the syntactic congruence for regular languages, such that this congruence is of finite index if, and only if, L is a Vpl. We then study the problem of finding canonical minimal deterministic automata for Vpls. Though Vpls in general do not have unique minimal automata, we consider a subclass of VPAs called kmodule singleentry VPAs that correspond to programs with recursive procedures without input parameters, and show that the class of wellmatched Vpls do indeed have unique minimal kmodule singleentry automata. We also give a polynomial time algorithm that minimizes such kmodule singleentry VPAs. 1 Introduction The class of visibly pushdown languages (Vpl), introduced in [1], is a subclassof contextfree languages accepted by pushdown automata in which the input letter determines the type of operation permitted on the stack. Visibly pushdown languages are closed under all boolean operations, and problems such as inclusion, that are undecidable for contextfree languages, are decidable for Vpl. Vpls are relevant to several applications that use contextfree languages suchas the modelchecking of software programs using their pushdown models [13]. Recent work has shown applications in other contexts: in modeling semanticsof effects in processing XML streams [4], in game semantics for programming languages [5], and in identifying larger classes of pushdown specifications thatadmit decidable problems for infinite games on pushdown graphs [6].
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 117 (15 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
The Boolean formula value problem is in ALOGTIME
 in Proceedings of the 19th Annual ACM Symposium on Theory of Computing
, 1987
"... The Boolean formula value problem is in alternating log time and, more generally, parenthesis contextfree languages are in alternating log time. The evaluation of reverse Polish notation Boolean formulas is also in alternating log time. These results are optimal since the Boolean formula value ..."
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Cited by 80 (7 self)
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The Boolean formula value problem is in alternating log time and, more generally, parenthesis contextfree languages are in alternating log time. The evaluation of reverse Polish notation Boolean formulas is also in alternating log time. These results are optimal since the Boolean formula value problem is complete for alternating log time under deterministic log time reductions. Consequently, it is also complete for alternating log time under AC reductions.
ContextFree Languages and PushDown Automata
 Handbook of Formal Languages
, 1997
"... Contents 1. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.1 Grammars : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.2 Examples : : : : : : : : : : : : : : : : : : : : : : : : : : : ..."
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Cited by 70 (0 self)
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Contents 1. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.1 Grammars : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.2 Examples : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2. Systems of equations : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.1 Systems : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.2 Resolution : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11 2.3 Linear systems : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12 2.4 Parikh's theorem : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
A Decision Procedure for a Class of Set Constraints
 In Fifth Annual IEEE Symposium on Logic in Computer Science
, 1991
"... A set constraint is of the form exp 1 ' exp 2 where exp 1 and exp 2 are set expressions constructed using variables, function symbols, projection symbols, and the set union, intersection and complement symbols. While the satisfiability problem for such constraints is open, restricted classes ha ..."
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Cited by 54 (0 self)
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A set constraint is of the form exp 1 ' exp 2 where exp 1 and exp 2 are set expressions constructed using variables, function symbols, projection symbols, and the set union, intersection and complement symbols. While the satisfiability problem for such constraints is open, restricted classes have been useful in program analysis. The main result herein is a decision procedure for definite set constraints which are of the restricted form a ' exp where a contains only constants, variables and function symbols, and exp is a positive set expression (that is, it does not contain the complement symbol). A conjunction of such constraints, whenever satisfiable, has a least model and the algorithm will output an explicit representation of this model. 1 1 Introduction We consider a formalism for elementary set algebra which is useful for describing properties of programs whose underlying domain of computation is a Herbrand universe. The domain of discourse for this formalism is the powerset of...
Sample Selection for Statistical Grammar Induction
 PROC. OF THE CONFERENCE ON EMPIRICAL METHODS IN NATURAL LANGUAGE PROCESSING (EMNLP
, 2000
"... Corpusbased grammar induction relies on using many handparsed sentences as training examples. However, the construction of a training corpus with detailed syntactic analysis for every sentence is a laborintensive task. We propose to use sample selection methods to minimize the amount of annotatio ..."
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Cited by 26 (3 self)
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Corpusbased grammar induction relies on using many handparsed sentences as training examples. However, the construction of a training corpus with detailed syntactic analysis for every sentence is a laborintensive task. We propose to use sample selection methods to minimize the amount of annotation needed in the training data, thereby reducing the workload of the human annotators. This paper shows that the amount of annotated train ing data can be reduced by 36% without degrading the quality of the induced grammars.
Learning of ContextFree Languages: A Survey of the Literature
 REP
, 1996
"... We survey methods for learning contextfree languages (CFL's) in the theoretical computer science literature. We first present some important negative results. Then, we consider five types of methods: those that take text as input, those that take structural information as input, those that rel ..."
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Cited by 24 (0 self)
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We survey methods for learning contextfree languages (CFL's) in the theoretical computer science literature. We first present some important negative results. Then, we consider five types of methods: those that take text as input, those that take structural information as input, those that rely on CFL formalisms that are not based on contextfree grammars, those which learn subclasses of CFL's, and stochastic methods. A description of the subclasses of CFL's considered is provided, as is an extensive bibliography.
Formal properties of XML grammars and languages
 Acta Inform
"... XML documents are described by a document type definition (DTD). An XMLgrammar is a formal grammar that captures the syntactic features of a DTD. We investigate properties of this family of grammars. We show that every XMLlanguage basically has a unique XMLgrammar. We give two characterizations o ..."
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Cited by 21 (0 self)
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XML documents are described by a document type definition (DTD). An XMLgrammar is a formal grammar that captures the syntactic features of a DTD. We investigate properties of this family of grammars. We show that every XMLlanguage basically has a unique XMLgrammar. We give two characterizations of languages generated by XMLgrammars, one is settheoretic, the other is by a kind of saturation property. We investigate decidability problems and prove that some properties that are undecidable for general contextfree languages become decidable for XMLlanguages. We also characterize those XMLgrammars that generate regular XMLlanguages. Résumé Les documents XML sont décrits par une définition de type de document (DTD). Une grammaire XML est une grammaire formelle qui retient les aspects syntaxiques d’une DTD. Nous étudions les propriétés de cette famille de grammaires. Nous montrons qu’un langage XML a essentiellement une seule grammaire XML. Nous donnons deux caractérisations des langages engendrés par les grammaires XML, la première est ensembliste, la deuxième est par une propriété de saturation. Nous examinons des problèmes de décision et nous prouvons que certaines propriétés qui sont indécidables pour les langages 1 contextfree généraux deviennent décidables pour les langages XML. Nous caractérisons également les grammaires XML qui engendrent des langages rationnels. 1
XML Grammars
, 2000
"... XML documents are described by a document type denition (DTD). An XMLgrammar is a formal grammar that captures the syntactic features of a DTD. We investigate properties of this family of grammars. We show that an XMLlanguage basically has a unique XMLgrammar. We give two characterizations of ..."
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XML documents are described by a document type denition (DTD). An XMLgrammar is a formal grammar that captures the syntactic features of a DTD. We investigate properties of this family of grammars. We show that an XMLlanguage basically has a unique XMLgrammar. We give two characterizations of languages generated by XMLgrammars, one is settheoretic, the other is by a kind of saturation property. We investigate decidability problems and prove that some properties that are undecidable for general contextfree languages become decidable for XMLlanguages.
Type Inference and Type Checking for Queries on Execution Traces
, 2008
"... This paper studies, for the first time, the management of type information for an important class of semistructured data: nested DAGs (Directed Acyclic Graphs) that describe execution traces of business processes (BPs for short). Specifically, we consider here type inference and type checking for q ..."
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This paper studies, for the first time, the management of type information for an important class of semistructured data: nested DAGs (Directed Acyclic Graphs) that describe execution traces of business processes (BPs for short). Specifically, we consider here type inference and type checking for queries over BP execution traces. The queries that we consider select portions of the traces that are of interest to the user; the types describe the possible shape of the execution traces in the input/output of the query. We formally define and characterize here three common classes of BP execution traces and their respective notions of type inference and type checking. We study the complexity of the two problems for query languages of varying expressive power and present efficient type inference/checking algorithms whenever possible. Our analysis offers a nearly complete picture of which combinations of trace classes and query features lead to PTIME algorithms and which to NPcomplete or undecidable problems.