Expressiveness and static analysis of extended conjunctive regular path queries

Freydenberger, Dominik D.; Schweikardt, Nicole

doi:10.1016/j.jcss.2013.01.008

Cited by 9 publications

(8 citation statements)

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“…Similar results were obtained for ECRPQs by Freydenberger and Schweikardt in [19] (see in particular Theorem 4.6 in that paper). Notably, the proofs of most results in [19] do not require the full power of ECRPQs, but use equality CRPQs instead.…”

Section: Adapting Undecidability Results For Ecprqs To Spannerssupporting

confidence: 87%

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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Section: Adapting Undecidability Results For Ecprqs To Spannerssupporting

confidence: 87%

A Logic for Document Spanners

Freydenberger

2018

Theory Comput Syst

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“…While there is no direct connection between ECRPQs and core spanners, both models share the basic idea of combining regular languages with a comparison operator that can express string equality. As shown by Freydenberger and Schweikardt [16], ECRPQs have undecidability results that are comparable to those in the present paper, and to those for xregexes (cf. Freydenberger [12]).…”

Section: Introductionsupporting

confidence: 90%

“…Note that in most of the cases, these lower bounds do not require the join operator, and mostly rely on the string equality selection. This can be interpreted as a sign that string equality (or repetition) is an expensive operator, in particular as similar results have been observed for related models (e. g., [2,12,16]). On the other hand, Proposition 4.2 demonstrates that even without string equality, join is also an expensive operator.…”

Section: Conclusion and Further Worksupporting

confidence: 71%

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Document Spanners: From Expressive Power to Decision Problems

Freydenberger

Holldack

2017

Theory Comput Syst

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We examine document spanners, a formal framework for information extraction that was introduced by Fagin, Vansummeren (PODS 2013, JACM 2015). A document spanner is a function that maps an input string to a relation over spans (intervals of positions of the string). We focus on document spanners that are defined by regex formulas, which are basically regular expressions that map matched subexpressions to corresponding spans, and on core spanners, which extend the former by standard algebraic operators and string equality selection. First, we compare the expressive power of core spanners to three models -namely, patterns, word equations, and a rich and natural subclass of extended regular expressions (regular expressions with a repetition operator). These results are then used to analyze the complexity of query evaluation and various aspects of static analysis of core spanners. Finally, we examine the relative succinctness of different kinds of representations of core spanners and relate this to the simplification of core spanners that are extended with difference operators.

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“…We will show that there are queries in PTIME expressible in WL but not in ERWL. This result is interesting, in view of the reported scarcity of techniques for showing nonexpressibility even by ECRPQs [23]. Our proof is an adaptation of de Rougemonts's Ehrenfeucht-Fraïssé game argument about Hamiltonicity [17].…”

Section: Introductionmentioning

confidence: 99%

Walk logic as a framework for path query languages on graph databases

Hellings

Kuijpers

Bussche

et al. 2013

Proceedings of the 16th International Conference on Database Theory

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Motivated by the current interest in languages for expressing path queries to graph databases, this paper proposes to investigate Walk Logic (WL): the extension of first-order logic on finite graphs with the possibility to explicitly quantify over walks. WL can serve as a unifying framework for path query languages. To support this claim, WL is compared in expressive power with various established query languages for graphs, such as first-order logic extended with reachability; the monadic second-order logic of graphs; hybrid computation tree logic; and regular path queries. WL also serves as a framework to investigate the following natural questions: Is quantifying over walks more powerful than quantifying over paths (walks without repeating nodes) only? Is quantifying over infinite walks more powerful than quantifying over finite walks only? WL model checking is decidable, but determining the precise complexity remains an open problem.

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Expressiveness and static analysis of extended conjunctive regular path queries

Cited by 9 publications

References 13 publications

A Logic for Document Spanners

A Logic for Document Spanners

Document Spanners: From Expressive Power to Decision Problems

Walk logic as a framework for path query languages on graph databases

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