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The monadic secondorder logic of graphs I. Recognizable sets of Finite Graphs
 Information and Computation
, 1990
"... The notion of a recognizable sef offinite graphs is introduced. Every set of finite graphs, that is definable in monadic secondorder logic is recognizable, but not vice versa. The monadic secondorder theory of a contextfree set of graphs is decidable. 0 19W Academic Press. Inc. This paper begins ..."
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Cited by 208 (14 self)
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The notion of a recognizable sef offinite graphs is introduced. Every set of finite graphs, that is definable in monadic secondorder logic is recognizable, but not vice versa. The monadic secondorder theory of a contextfree set of graphs is decidable. 0 19W Academic Press. Inc. This paper begins an investigation of the monadic secondorder logic of graphs and of sets of graphs, using techniques from universal algebra, and the theory of formal languages. (By a graph, we mean a finite directed hyperedgelabelled hypergraph, equipped with a sequence of distinguished vertices.) A survey of this research can be found in Courcelle [ 111. An algebraic structure on the set of graphs (in the above sense) has been proposed by Bauderon and Courcelle [2,7]. The notion of a recognizable set of finite graphs follows, as an instance of the general notion of recognizability introduced by Mezei and Wright in [25]. A graph can also be considered as a logical structure of a certain type. Hence, properties of graphs can be written in firstorder logic or in secondorder logic. It turns out that monadic secondorder logic, where quantifications over sets of vertices and sets of edges are used, is a reasonably powerful logical language (in which many usual graph properties can be written), for which one can obtain decidability results. These decidability results do not hold for secondorder logic, where quantifications over binary relations can also be used. Our main theorem states that every definable set of finite graphs (i.e., every set that is the set of finite graphs satisfying a graph property expressible in monadic secondorder logic) is recognizable. * This work has been supported by the “Programme de Recherches Coordonntes: Mathematiques et Informatique.”
The Expression Of Graph Properties And Graph Transformations In Monadic SecondOrder Logic
, 1997
"... By considering graphs as logical structures, one... ..."
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Cited by 147 (39 self)
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By considering graphs as logical structures, one...
Regular Tree and Regular Hedge Languages over Unranked Alphabets: Version 1
, 2001
"... We survey the basic results on regular tree languages over unranked alphabets; that is, we use an unranked alphabet for the labels of nodes, we allow unbounded, yet regular, degree nodes and we treat sequences of trees that, following Courcelle, we call hedges. The survey was begun by the first ..."
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Cited by 107 (5 self)
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We survey the basic results on regular tree languages over unranked alphabets; that is, we use an unranked alphabet for the labels of nodes, we allow unbounded, yet regular, degree nodes and we treat sequences of trees that, following Courcelle, we call hedges. The survey was begun by the first and third authors. Subsequently, when they discovered that the second author had already written a summary of this view of tree automata and languages, the three authors decided to join forces and produce a consistent review of the area. The survey is still unfinished because we have been unable to find the time to finish it. We are making it available in this unfinished form as a research report because it has, already, been heavily cited in the literature.
Training Tree Transducers
 IN HLTNAACL
, 2004
"... Many probabilistic models for natural language are now written in terms of hierarchical tree structure. Treebased modeling still lacks many of the standard tools taken for granted in (finitestate) stringbased modeling. The theory of tree transducer automata provides a possible framework to ..."
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Cited by 102 (10 self)
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Many probabilistic models for natural language are now written in terms of hierarchical tree structure. Treebased modeling still lacks many of the standard tools taken for granted in (finitestate) stringbased modeling. The theory of tree transducer automata provides a possible framework to draw on, as it has been worked out in an extensive literature. We motivate the use of tree transducers for natural language and address the training problem for probabilistic treetotree and treetostring transducers.
Symbolic model checking with rich assertional languages
 Theoretical Computer Science
, 1997
"... Abstract. The paper shows that, by an appropriate choice of a rich assertional language, it is possible to extend the utility of symbolic model checking beyond the realm of bddrepresented nitestate systems into the domain of in nitestate systems, leading to a powerful technique for uniform veri c ..."
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Cited by 89 (4 self)
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Abstract. The paper shows that, by an appropriate choice of a rich assertional language, it is possible to extend the utility of symbolic model checking beyond the realm of bddrepresented nitestate systems into the domain of in nitestate systems, leading to a powerful technique for uniform veri cation of unbounded (parameterized) process networks. The main contributions of the paper are a formulation of a general framework for symbolic model checking of in nitestate systems, a demonstration that many individual examples of uniformly veri ed parameterized designs that appear in the literature are special cases of our general approach, verifying the correctness of the Futurebus+ design for all singlebus con gurations, extending the technique to tree architectures, and establishing that the presented method is a precise dual to the topdown invariant generation method used in deductive veri cation. 1
Monadic Datalog and the Expressive Power of Languages for Web Information Extraction
 J. ACM
, 2002
"... Research on information extraction from Web pages (wrapping) has seen much activity in recent times (particularly systems implementations), but little work has been done on formally studying the expressiveness of the formalisms proposed or on the theoretical foundations of wrapping. In this paper, w ..."
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Cited by 75 (11 self)
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Research on information extraction from Web pages (wrapping) has seen much activity in recent times (particularly systems implementations), but little work has been done on formally studying the expressiveness of the formalisms proposed or on the theoretical foundations of wrapping. In this paper, we first study monadic datalog as a wrapping language (over ranked or unranked tree structures). Using previous work by Neven and Schwentick, we show that this simple language is equivalent to full monadic second order logic (MSO) in its ability to specify wrappers. We believe that MSO has the right expressiveness required for Web information extraction and thus propose MSO as a yardstick for evaluating and comparing wrappers. Using the above result, we study the kernel fragment Elog of the Elog wrapping language used in the Lixto system (a visual wrapper generator). The striking fact here is that Elog exactly captures MSO, yet is easier to use. Indeed, programs in this language can be entirely visually specified. We also formally compare Elog to other wrapping languages proposed in the literature.
MONA Implementation Secrets
, 2000
"... The MONA tool provides an implementation of the decision procedures for the logics WS1S and WS2S. It has been used for numerous applications, and it is remarkably efficient in practice, even though it faces a theoretically nonelementary worstcase complexity. The implementation has matured over a p ..."
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Cited by 70 (6 self)
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The MONA tool provides an implementation of the decision procedures for the logics WS1S and WS2S. It has been used for numerous applications, and it is remarkably efficient in practice, even though it faces a theoretically nonelementary worstcase complexity. The implementation has matured over a period of six years. Compared to the first naive version, the present tool is faster by several orders of magnitude. This speedup is obtained from many different contributions working on all levels of the compilation and execution of formulas. We present a selection of implementation "secrets" that have been discovered and tested over the years, including formula reductions, DAGification, guided tree automata, threevalued logic, eager minimization, BDDbased automata representations, and cacheconscious data structures. We describe these techniques and quantify their respective effects by experimenting with separate versions of the MONA tool that in turn omit each of them.
Efficient Static Analysis of XML Paths and Types
, 2008
"... We present an algorithm to solve XPath decision problems under regular tree type constraints and show its use to statically typecheck XPath queries. To this end, we prove the decidability of a logic with converse for finite ordered trees whose time complexity is a simple exponential of the size of ..."
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Cited by 60 (33 self)
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We present an algorithm to solve XPath decision problems under regular tree type constraints and show its use to statically typecheck XPath queries. To this end, we prove the decidability of a logic with converse for finite ordered trees whose time complexity is a simple exponential of the size of a formula. The logic corresponds to the alternation free modal µcalculus without greatest fixpoint, restricted to finite trees, and where formulas are cyclefree. Our proof method is based on two auxiliary results. First, XML regular tree types and XPath expressions have a linear translation to cyclefree formulas. Second, the least and greatest fixpoints are equivalent for finite trees, hence the logic is closed under negation. Building on these results, we describe a practical, effective system for solving the satisfiability of a formula. The system has been experimented with some decision problems such as XPath emptiness, containment, overlap, and coverage, with or without type constraints. The benefit of the approach is that our system can be effectively used in static analyzers for programming languages
XPath with conditional axis relations
 In EDBT
, 2004
"... This paper is about the W3C standard nodeaddressing language for XML documents, called XPath. XPath is still under development. Version 2.0 appeared in 2001 while the theoretical foundations of Version 1.0 (dating from 1998) are still being widely studied. The paper aims at bringing XPath to a " ..."
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Cited by 55 (6 self)
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This paper is about the W3C standard nodeaddressing language for XML documents, called XPath. XPath is still under development. Version 2.0 appeared in 2001 while the theoretical foundations of Version 1.0 (dating from 1998) are still being widely studied. The paper aims at bringing XPath to a "stable fixed point" in its development: a version which is expressively complete, still manageable computationally, with a userfriendly syntax and a natural semantics.
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 have be ..."
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Cited by 53 (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...