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The FirstOrder Theory of Ordering Constraints over Feature Trees
 Discrete Mathematics and Theoretical Computer Science
, 2001
"... The system FT of ordering constraints over feature trees has been introduced as an extension of the system FT of equality constraints over feature trees. We investigate the firstorder theory of FT and its fragments, both over finite trees and over possibly infinite trees. We prove that the firstor ..."
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Cited by 19 (5 self)
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The system FT of ordering constraints over feature trees has been introduced as an extension of the system FT of equality constraints over feature trees. We investigate the firstorder theory of FT and its fragments, both over finite trees and over possibly infinite trees. We prove that the firstorder theory of FT is undecidable, in contrast to the firstorder theory of FT which is wellknown to be decidable. We determine the complexity of the entailment problem of FT with existential quantification to be PSPACEcomplete, by proving its equivalence to the inclusion problem of nondeterministic finite automata. Our reduction from the entailment problem to the inclusion problem is based on a new alogrithm that, given an existential formula of FT , computes a finite automaton which accepts all its logic consequences.
Ordering Constraints over Feature Trees
, 1999
"... Feature trees are the formal basis for algorithms manipulating record like structures in constraint programming, computational linguistics and in concrete applications like software configuration management. Feature trees model records, and constraints over feature trees yield extensible and modular ..."
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Cited by 14 (5 self)
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Feature trees are the formal basis for algorithms manipulating record like structures in constraint programming, computational linguistics and in concrete applications like software configuration management. Feature trees model records, and constraints over feature trees yield extensible and modular record descriptions. We introduce the constraint system FT of ordering constraints interpreted over feature trees. Under the view that feature trees represent symbolic information, the relation corresponds to the information ordering ("carries less information than"). We present two algorithms in cubic time, one for the satisfiability problem and one for the entailment problem of FT . We show that FT has the independence property. We are thus able to handle negative conjuncts via entailment and obtain a cubic algorithm that decides the satisfiability of conjunctions of positive and negated ordering constraints over feature trees. Furthermore, we reduce the satisfiability problem of Dorre's weak subsumption constraints to the satisfiability problem of FT and improve the complexity bound for solving weak subsumption constraints from O(n^5) to O(n³).
Dominance Constraints in Context Unification
, 1998
"... Tree descriptions based on dominance constraints are popular in several areas of computational linguistics including syntax, semantics, and discourse. Tree descriptions in the language of context unification have attracted some interest in unification and rewriting theory. Recently, dominance constr ..."
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Cited by 14 (10 self)
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Tree descriptions based on dominance constraints are popular in several areas of computational linguistics including syntax, semantics, and discourse. Tree descriptions in the language of context unification have attracted some interest in unification and rewriting theory. Recently, dominance constraints and context unification have both been used in different underspecified approaches to the semantics of scope, parallelism, and their interaction. This raises the question whether both description languages are related. In this paper, we show for a first time that dominance constraints can be expressed in context unification. We also prove that dominance constraints extended with parallelism constraints are equal in expressive power to context unification.
Tree Extension Algebras: Logics, Automata, and Query Languages
 In Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science (LICS
, 2002
"... We study relations on trees defined by firstorder constraints over a vocabulary that includes the tree extension relation T T , holding if and only if every branch of T extends to a branch of T , unary nodetests, and a binary relation checking if the domains of two trees are equal. We show ..."
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Cited by 8 (1 self)
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We study relations on trees defined by firstorder constraints over a vocabulary that includes the tree extension relation T T , holding if and only if every branch of T extends to a branch of T , unary nodetests, and a binary relation checking if the domains of two trees are equal. We show that from such a formula one can generate a tree automaton that accepts the set of tuples of trees defined by the formula, and conversely that every automaton over treetuples is captured by such a formula. We look at the fragment with only extension inequalities and leaf tests, and show that it corresponds to a new class of automata on tree tuples, which is strictly weaker then general treetuple automata. We use the automata representations to show separation and expressibility results for formulae in the logic. We then turn to relational calculi over the logic defined here: that is, from constraints we extend to queries that have secondorder parameters for a finite set of tree tuples. We give normal forms for queries, and use these to get bounds on the data complexity of query evaluation, showing that while general query evaluation is unbounded within the polynomial hierarchy, generic query evaluation has very low complexity, giving strong bounds on the expressive power of relational calculi with tree extension constraints. We also give normal forms for safe queries in the calculus.
Logical definability and query languages over ranked and unranked trees
 ACM TOCL
"... We study relations on trees defined by firstorder constraints over a vocabulary that includes the tree extension relation T ≺ T ′ , holding if and only if every branch of T extends to a branch of T ′, unary nodetests, and a binary relation checking if the domains of two trees are equal. We conside ..."
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Cited by 7 (4 self)
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We study relations on trees defined by firstorder constraints over a vocabulary that includes the tree extension relation T ≺ T ′ , holding if and only if every branch of T extends to a branch of T ′, unary nodetests, and a binary relation checking if the domains of two trees are equal. We consider both ranked and unranked trees. These are trees with and without a restriction on the number of children of nodes. We adopt the modeltheoretic approach to tree relations and study relations definable over the structure consisting of the set of all trees and the above predicates. We relate definability of sets and relations of trees to computability by tree automata. We show that some natural restrictions correspond to familiar logics in the more classical setting, where every tree is a structure over a fixed vocabulary, and to logics studied in the context of XML pattern languages. We then look at relational calculi over collections of trees, and obtain quantifierrestriction results that give us bounds on the expressive power and complexity. As unrestricted relational calculi can express problems complete for each level of the polynomial hierarchy, we look at their restrictions, corresponding to the restricted logics over the family of all unranked trees, and find several calculi with low (NC 1) data complexity, while still expressing properties important for database and
Type Inference for FirstClass Messages with Feature Constraints
 International Journal of Foundations of Computer Science
, 1998
"... We present a constraint system OF of feature trees that is appropriate to specify and implement type inference for firstclass messages. OF extends traditional systems of feature constraints by a selection constraint xhyiz "by firstclass feature tree" y, in contrast to the standard selection con ..."
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Cited by 5 (0 self)
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We present a constraint system OF of feature trees that is appropriate to specify and implement type inference for firstclass messages. OF extends traditional systems of feature constraints by a selection constraint xhyiz "by firstclass feature tree" y, in contrast to the standard selection constraint x[ f ]y "by fixed feature" f . We investigate the satisfiability problem of OF and show that it can be solved in polynomial time, and even in quadratic time in an important special case. We compare OF with Treinen's constraint system EF of feature constraints with firstclass features, which has an NPcomplete satisfiability problem. This comparison yields that the satisfiability problem for OF with negation is NPhard. Based on OF we give a simple account of type inference for firstclass messages in the spirit of Nishimura's recent proposal, and we show that it has polynomial time complexity: We also highlight an immediate extension that is desirable but makes type inference NPhard.
Logical Definability and Query Languages over Unranked Trees
 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science (LICS
, 2003
"... Unranked trees, that is, trees with no restriction on the number of children of nodes, have recently attracted much attention, primarily as an abstraction of XML documents. In this paper, we study logical definability over unranked trees, as well as collections of unranked trees, that can be viewed ..."
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Cited by 4 (1 self)
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Unranked trees, that is, trees with no restriction on the number of children of nodes, have recently attracted much attention, primarily as an abstraction of XML documents. In this paper, we study logical definability over unranked trees, as well as collections of unranked trees, that can be viewed as databases of XML documents. The traditional approach to definability is to view each tree as a structure of a fixed vocabulary, and study the expressive power of various logics on trees. A different approach, based on model theory, considers a structure whose universe is the set of all trees, and studies definable sets and relations; this approach extends smoothly to the setting of definability over collections of trees. We study the latter, modeltheoretic approach. We find sets of operations on unranked trees that define regular tree languages, and show that some natural restrictions correspond to logics studied in the context of XML pattern languages. We then look at relational calculi over collections of unranked trees, and obtain quantifierrestriction results that give us bounds on the expressive power and complexity. As unrestricted relational calculi can express problems complete for each level of the polynomial hierarchy, we look at their restrictions, corresponding to the restricted logics over the family of all unranked trees, and find several calculi with low (NC ) data complexity, that can express important XML properties like DTD validation and XPath evaluation.