Dominance Constraints: Algorithms and Complexity

Koller, Alexander; Niehren, Joachim; Treinen, Ralf

doi:10.1007/3-540-45738-0_7

Cited by 22 publications

(28 citation statements)

References 9 publications

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“…if p =˙ then n ≺ n and there is an n such that n n and n n , (7) if p =˙ then n ≺ n and there is an n such that n n and n n , (8) if p = ⇑ then n = r, (9) if p = t ∈ Σ then n = n and λ(n) = t, (10) …”

Section: Initial Definitionsmentioning

confidence: 99%

“…Before we discuss the problem of deciding satisfiability of XPath expressions we consider the same problem for a related notion called partial tree descriptions which has been studied in computational linguistics [14,5,10,4]. A partial tree description can be informally described as a formula in EFO (Existential First Order Logic) that quantifies over the nodes in the tree and uses the binary predicates =, , + , * and ≺ and a special constant r (the root).…”

Section: Tree Description Graphsmentioning

confidence: 99%

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Satisfiability of XPath Expressions

Hidders

2004

Database Programming Languages

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In this paper, we investigate the complexity of deciding the satisfiability of XPath 2.0 expressions, i.e., whether there is an XML document for which their result is nonempty. Several fragments that allow certain types of expressions are classified as either in PTIME or NP-hard to see which type of expression make this a hard problem. Finally, we establish a link between XPath expressions and partial tree descriptions which are studied in computational linguistics.

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Section: Initial Definitionsmentioning

confidence: 99%

Section: Tree Description Graphsmentioning

confidence: 99%

Satisfiability of XPath Expressions

Hidders

2004

Database Programming Languages

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“…In [ENRX98] it is proved that parallelism constraints -a kind of partial description of trees-are equivalent to context unification. Dominance constraints are a subset of parallelism constraints, and their solvability is decidable [KNT98]. Other application areas of context unification include computational linguistics [NPR97b].…”

Section: Introductionmentioning

confidence: 99%

Context Unification and Traversal Equations

Levy

Villaret

2001

Rewriting Techniques and Applications

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Abstract. Context unification was originally defined by H. Comon in ICALP'92, as the problem of finding a unifier for a set of equations containing first-order variables and context variables. These context variables have arguments, and can be instantiated by contexts. In other words, they are second-order variables that are restricted to be instantiated by linear terms (a linear term is a λ-expression λx 1 · · · λxn . t where every xi occurs exactly once in t). In this paper, we prove that, if the so called rank-bound conjecture is true, then the context unification problem is decidable. This is done reducing context unification to solvability of traversal equations (a kind of word unification modulo certain permutations) and then, reducing traversal equations to word equations with regular constraints.

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“…Their satisfiability problem is NP-complete [9]. Whether dominance constraints can be expressed in any of the decidable fragments of CU was left open.…”

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confidence: 99%

“…In this paper, we introduce the once-only SO-nesting fragment of stratified CU, and show how to express dominance constraints there. Since satisfiability of dominance constraints is NP-hard [9], it follows that the once-only SO-nesting fragment of stratified CU is NP-complete. We also characterize the precise part of the once-only SO-nesting fragment that is equivalent to dominance constraints.…”

mentioning

confidence: 99%