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240
Caterpillars: A Context Specification Technique
 Markup Languages
, 2000
"... We present a novel, yet simple, technique for the specification of context in structured documents that we call caterpillar expressions. Although we are primarily applying this technique in the specification of contextdependent style sheets for HTML, SGML and XML documents, it can also be used f ..."
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Cited by 35 (7 self)
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We present a novel, yet simple, technique for the specification of context in structured documents that we call caterpillar expressions. Although we are primarily applying this technique in the specification of contextdependent style sheets for HTML, SGML and XML documents, it can also be used for query specification for structured documents, as we shall demonstrate, and for the specification of computer program transformations. From a conceptual point of view, structured documents are trees, and one of the oldest and bestestablished techniques to process trees and, hence, structured documents are tree automata. We present a number of theoretical results that allow us to compare the expressive power of caterpillar expressions and caterpillar automata, their companions, to the expressive power of tree automata. In particular, we demonstrate that each caterpillar expression describes a regular tree language that is, hence, recognizable by a tree automaton. Finally, we empl...
Finite Representation of Infinite Query Answers
, 1992
"... : We define here a formal notion of finite representation of infinite query answers in logic programs. We apply this notion to Datalog nS (Datalog with n successors): an extension of Datalog capable of representing infinite phenomena like flow of time or plan construction. Predicates in Datalog nS ..."
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Cited by 31 (5 self)
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: We define here a formal notion of finite representation of infinite query answers in logic programs. We apply this notion to Datalog nS (Datalog with n successors): an extension of Datalog capable of representing infinite phenomena like flow of time or plan construction. Predicates in Datalog nS can have arbitrary unary and limited nary function symbols in one fixed position. This class of logic programs is known to be decidable. However, least Herbrand models of Datalog nS programs may be infinite and consequently queries may have infinite answers. We present a method to finitely represent infinite least Herbrand models of Datalog nS programs as relational specifications. A relational specification consists of a finite set of facts and a finitely specified congruence relation. A relational specification has the following desirable properties. First, it is explicit in the sense that once it is computed, the original Datalog nS program (and its underlying computational engine) can ...
Interconvertibility of a Class of Set Constraints and ContextFreeLanguage Reachability
 TCS
, 1998
"... We show the interconvertibility of contextfreelanguage reachability problems and a class of setconstraint problems: given a contextfreelanguage reachability problem, we show how to construct a setconstraint problem whose answer gives a solution to the reachability problem; given a setconstra ..."
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Cited by 31 (2 self)
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We show the interconvertibility of contextfreelanguage reachability problems and a class of setconstraint problems: given a contextfreelanguage reachability problem, we show how to construct a setconstraint problem whose answer gives a solution to the reachability problem; given a setconstraint problem, we show how to construct a contextfreelanguage reachability problem whose answer gives a solution to the setconstraint problem. The interconvertibility of these two formalisms offers an conceptual advantage akin to the advantage gained from the interconvertibility of finitestate automata and regular expressions in formal language theory, namely, a problem can be formulated in whichever formalism is most natural. It also offers some insight into the "O(n ) bottleneck" for different types of programanalysis problems and allows results previously obtained for contextfreelanguage reachability problems to be applied to setconstraint problems and vice versa.
Interconvertibility of Set Constraints and ContextFree Language Reachability
 In Proceedings of the ACM SIGPLAN Symposium on Partial Evaluation and SemanticsBased Program Manipulation
, 1996
"... We show the interconvertibility of contextfreelanguage reachability problems and a class of setconstraint problems: given a contextfreelanguage reachability problem, we show how to construct a setconstraint problem whose answer gives a solution to the reachability problem; given a setconstrai ..."
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Cited by 30 (1 self)
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We show the interconvertibility of contextfreelanguage reachability problems and a class of setconstraint problems: given a contextfreelanguage reachability problem, we show how to construct a setconstraint problem whose answer gives a solution to the reachability problem; given a setconstraint problem, we show how to construct a contextfreelanguage reachability problem whose answer gives a solution to the setconstraint problem. The interconvertibility of these two formalisms offers an conceptual advantage akin to the advantage gained from the interconvertibility of finitestate automata and regular expressions in formal language theory, namely, a problem can be formulated in whichever formalism is most natural. It also offers some insight into the "O(n&sup3;) bottleneck" for different types of programanalysis problems, and allows results previously obtained for contextfreelanguage reachability problems to be applied to setconstraint problems.
Capturing Practical Natural Language Transformations
"... We study automata for capturing transformations employed by practical natural language processing systems, such as those that translate between human languages. For several variations of finitestate string and tree transducers, we ask formal questions about expressiveness, modularity, teachability, ..."
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Cited by 28 (0 self)
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We study automata for capturing transformations employed by practical natural language processing systems, such as those that translate between human languages. For several variations of finitestate string and tree transducers, we ask formal questions about expressiveness, modularity, teachability, and generalization.
EQUIVALENCES AND TRANSFORMATIONS OF REGULAR SYSTEMS  APPLICATIONS TO RECURSIVE PROGRAM SCHEMES AND GRAMMARS
, 1986
"... This work presents a unified theory of recursive program schemes, contextfree grammars, grammars on arbitrary algebraic structures and, in fact, recursive definitions of all kind by means of regular systems. The equivalences of regular systems associated with either all their solutions or their le ..."
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Cited by 27 (5 self)
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This work presents a unified theory of recursive program schemes, contextfree grammars, grammars on arbitrary algebraic structures and, in fact, recursive definitions of all kind by means of regular systems. The equivalences of regular systems associated with either all their solutions or their least solutions (in all domains of appropriate type satisfying a set of algebraic laws expressed by equations) are systematically investigated and characterized (in some cases) in terms of system transformations by folding, unfolding and rewriting according to the equational algebraic laws. Grammars are better characterized in terms of polynomial systems which are regular systems involving the operation of set union, and the same questions are raised for them. We also examine conditions insuring the uniqueness of the solution of a regular or of a polynomial system. This theory applies to grammars of many kinds which generate trees, graphs, etc. We formulate some classical transformations of contextfree grammars in terms of correct transformations which only use folding, unfolding and algebraic laws and we immediately obtain their correctness.
Logical Specifications of Infinite Computations
 A Decade of Concurrency: Reflections and Perspectives, volume 803 of LNCS
, 1993
"... . Starting from an identification of infinite computations with ! words, we present a framework in which different classification schemes for specifications are naturally compared. Thereby we connect logical formalisms with hierarchies of descriptive set theory (e.g., the Borel hierarchy), of recu ..."
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Cited by 26 (2 self)
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. Starting from an identification of infinite computations with ! words, we present a framework in which different classification schemes for specifications are naturally compared. Thereby we connect logical formalisms with hierarchies of descriptive set theory (e.g., the Borel hierarchy), of recursion theory, and with the hierarchy of acceptance conditions of !automata. In particular, it is shown in which sense these hierarchies can be viewed as classifications of logical formulas by the complexity measure of quantifier alternation. In this context, the automaton theoretic approach to logical specifications over !words turns out to be a technique to reduce quantifier complexity of formulas. Finally, we indicate some perspectives of this approach, discuss variants of the logical framework (firstorder logic, temporal logic), and outline the effects which arise when branching computations are considered (i.e., when infinite trees instead of !words are taken as model of computation)...
Deterministic Automata on Unranked Trees
 In Proceedings of the 15th International Symposium on Fundamentals of Computation Theory (FCT), LNCS
, 2005
"... Abstract. We investigate bottomup and topdown deterministic automata on unranked trees. We show that for an appropriate denition of bottomup deterministic automata it is possible to minimize the number of states eciently and to obtain a unique canonical representative of the accepted tree langua ..."
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Cited by 26 (1 self)
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Abstract. We investigate bottomup and topdown deterministic automata on unranked trees. We show that for an appropriate denition of bottomup deterministic automata it is possible to minimize the number of states eciently and to obtain a unique canonical representative of the accepted tree language. For topdown deterministic automata it is well known that they are less expressive than the nondeterministic ones. By generalizing a corresponding proof from the theory of ranked tree automata we show that it is decidable whether a given regular language of unranked trees can be recognized by a topdown deterministic automaton. The standard deterministic topdown model is slightly weaker than the model we use, where at each node the automaton can scan the sequence of the labels of its successors before deciding its next move. 1
Regular Tree Languages Over NonRanked Alphabets
, 1998
"... F64.24> ffl denotes the empty string. Definition 1.1 We define the set of nodes nodes(t) of a tree t as a set of strings of natural numbers. The definition is by induction on t. 1. For a tree a() with just one node labelled a we define nodes(a()) = ffflg: 2. For a tree a(t 1 ; : : : ; t n ), ..."
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Cited by 26 (0 self)
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F64.24> ffl denotes the empty string. Definition 1.1 We define the set of nodes nodes(t) of a tree t as a set of strings of natural numbers. The definition is by induction on t. 1. For a tree a() with just one node labelled a we define nodes(a()) = ffflg: 2. For a tree a(t 1 ; : : : ; t n ), n 1, we define nodes(a(t 1 ; : : : ; t n ) = [ 1in i \Delta nodes(t i ) [ ffflg: The nodes of a tree viewed as a term correspond to occurrences of subterms. We denote nodes of trees with .