Document Spanners: From Expressive Power to Decision Problems

Freydenberger, Dominik D.; Holldack, Mario

doi:10.1007/s00224-017-9770-0

Cited by 25 publications

(53 citation statements)

References 30 publications

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“…Proof. The upper bound is obvious (even for core spanners, see [16]). For the lower bound, we construct a reduction from 3CNF-satisfiability to the evaluation problem of Boolean regex CQs.…”

Section: Lower Boundsmentioning

confidence: 99%

“…Theorem 5.1. [16] Evaluation of Boolean regex CQs with string equalities is NP-complete, even if restricted to queries of the form π ∅ ζ = x1,y1 · · · ζ = xm,ym α. In other words, even a single regex formula already leads to NP-hardness.…”

Section: Lower Boundmentioning

confidence: 99%

“…In other words, even a single regex formula already leads to NP-hardness. The proof from [16] uses a reduction from the membership problem for so-called pattern languages. It was shown by Fernau et al [14] that this membership problem is W[1]-complete for various parameters.…”

Section: Lower Boundmentioning

confidence: 99%

“…Hence, while a regex CQ that consists of a single regex formula can be evaluated efficiently (due to Lemmas 3.4 and 3.8 and Theorem 3.3), even limited use of string equalities can become expensive. This result can be obtained by combining the reduction from [14] with the reduction from [16], the former proof requires encodings that are needlessly complicated for our purposes (this is caused by the comparatively low expressive power of pattern languages). Instead, we take the basic idea of an FPT-reduction from the k-clique problem, and give a direct proof that is less technical.…”

Section: Lower Boundmentioning

confidence: 99%

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Joining Extractions of Regular Expressions

Freydenberger

Kimelfeld

Peterfreund

2018

Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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Regular expressions with capture variables, also known as "regex formulas," extract relations of spans (interval positions) from text. These relations can be further manipulated via Relational Algebra as studied in the context of document spanners, Fagin et al.'s formal framework for information extraction. We investigate the complexity of querying text by Conjunctive Queries (CQs) and Unions of CQs (UCQs) on top of regex formulas. We show that the lower bounds (NPcompleteness and W[1]-hardness) from the relational world also hold in our setting; in particular, hardness hits already single-character text! Yet, the upper bounds from the relational world do not carry over. Unlike the relational world, acyclic CQs, and even gamma-acyclic CQs, are hard to compute. The source of hardness is that it may be intractable to instantiate the relation defined by a regex formula, simply because it has an exponential number of tuples. Yet, we are able to establish general upper bounds. In particular, UCQs can be evaluated with polynomial delay, provided that every CQ has a bounded number of atoms (while unions and projection can be arbitrary). Furthermore, UCQ evaluation is solvable with FPT (Fixed-Parameter Tractable) delay when the parameter is the size of the UCQ.

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Section: Lower Boundsmentioning

confidence: 99%

Section: Lower Boundmentioning

confidence: 99%

Section: Lower Boundmentioning

confidence: 99%

Section: Lower Boundmentioning

confidence: 99%

See 2 more Smart Citations

Joining Extractions of Regular Expressions

Freydenberger

Kimelfeld

Peterfreund

2018

Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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“…The main topic of this paper is a logic that captures core spanners. Freydenberger and Holldack [16] connected core spanners to EC reg , the existential theory of concatenation with regular constraints. Described very informally, EC reg is a logic that combines equations on words (like xaby = ybax) with positive logical connectives, and regular languages that constrain variable replacement.…”

Section: Introductionmentioning

confidence: 99%

A Logic for Document Spanners

Freydenberger

2018

Theory Comput Syst

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Document spanners are a formal framework for information extraction that was introduced by Fagin, Kimelfeld, Reiss, and Vansummeren (PODS 2013, JACM 2015). One of the central models in this framework are core spanners, which formalize the query language AQL that is used in IBM's SystemT. As shown by Freydenberger and Holldack (ICDT 2016, ToCS 2018, there is a connection between core spanners and EC reg , the existential theory of concatenation with regular constraints. The present paper further develops this connection by defining SpLog, a fragment of EC reg that has the same expressive power as core spanners. This equivalence extends beyond equivalence of expressive power, as we show the existence of polynomial time conversions between SpLog and core spanners. Consequences and applications include an alternative way of defining relations for spanners, a pumping lemma for core spanners, and insights into the relative succinctness of various classes of spanner representations and their connection to graph querying languages. We also briefly discuss the connection between SpLog with negation and core spanners with a difference operator.Theory Comput Syst 2 More specifically, the distinction between these two definitions is only meaningful when dealing with constraints on variables that do not occur in word equations (like in formulas that consist only of constraint symbols). From an EC reg point of view, this are possible (although not of particular importance); but for spanners, these are not relevant. Theory Comput SystExample 2.1 Consider the EC-formula ϕ 1 (x, y, z) := ∃x,ŷ : (x = zx ∧ y = zŷ) and the EC reg -formula ϕ 2 (x, y, z) := ∃x,ŷ : (x = zx ∧ y = zŷ ∧ C + (z)) . Then σ |= ϕ 1 if and only if σ (x) and σ (y) have σ (z) as common prefix. If, in addition to this, σ (z) = ε, then σ |= ϕ 2 .Word equations and EC have the same expressive power (cf. Choffrut and Karhumäki [6] or Karhumäki, Mignosi, and Plandowski [30]). More formally, for every EC-formula ϕ, one can construct a word equation η with var(η) ⊇ free(ϕ), such that σ |= ϕ if and only if there is a σ with σ |= η and σ (x) = σ (x) for all x ∈ free(ϕ). This can directly be extended to convert any EC reg -formula into a word equation with constraints (cf. Diekert [10]). For conjunctions, the construction is easily explained: Choose distinct a, b ∈ . Hmelevskii's pattern pairing function is defined by α, β := αaβαbβ. Then (α L = α R ) ∧ (β L = β R ) holds if and only if α L , β L = α R , β R . This follows from a simple length argument, where the terminals a and b act as "barriers" that prevent unintended equalities (see Section 5.3 of [6] for details). The construction for disjunctions is similar, but it is also more involved and introduces new variables. Furthermore, converting alternating disjunctions and conjunctions may increase the size exponentially. Document Spanners Spanners and Primitive Spanner RepresentationsLet w := a 1 a 2 · · · a n be a word over , with n ≥ 0 and a 1 , . . . , a n ∈ . A span of w is an interval [i, j with 1 ≤ i ≤ j ≤ n + 1...

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Matching Patterns with Variables

Manea

Schmid

2019

Lecture Notes in Computer Science

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A pattern α (i. e., a string of variables and terminals) matches a word w, if w can be obtained by uniformly replacing the variables of α by terminal words. The respective matching problem, i. e., deciding whether or not a given pattern matches a given word, is generally NP-complete, but can be solved in polynomial-time for classes of patterns with restricted structure. In this paper we overview a series of recent results related to efficient matching for patterns with variables, as well as a series of extensions of this problem.

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Document Spanners: From Expressive Power to Decision Problems

Cited by 25 publications

References 30 publications

Joining Extractions of Regular Expressions

Joining Extractions of Regular Expressions

A Logic for Document Spanners

Matching Patterns with Variables

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