Small Dynamic Complexity Classes

Zeume, Thomas

doi:10.1007/978-3-662-54314-6

Cited by 4 publications

(5 citation statements)

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“…Let R γ + be the spanner relation for Σ * • x{γ + } • Σ * . We know from Proposition 5.7 that we can maintain this in DynPROP, and therefore, due to [110], we can maintain this in DynCQ. However, it follows that…”

Section: Base Case 2 (X ∈ γ) For Every X ∈ Vars (ψ) and Every Regular...mentioning

confidence: 92%

“…Of particular interest to this chapter are the classes DynCQ and DynUCQ, where the update formulas are conjunctive queries or unions of conjunctive queries. As shown by Zeume and Schwentick [111], DynCQ = DynUCQ holds; but it is open whether these are proper subclasses of DynFO (see Zeume [110] for detailed background information).…”

Section: Chapter 5 Dynamic Complexitymentioning

confidence: 99%

“…We use Proposition 5.7 along with the fact that DynPROP is a strict subclass of DynCQ (see Theorem 3.1.5 part b of [110]). However, note that from the proof of Base case 1, the way we handle the empty word in spanners, and EP-FC[REG] relations differs slightly.…”

Section: Base Case 2 (X ∈ γ) For Every X ∈ Vars (ψ) and Every Regular...mentioning

confidence: 99%

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Conjunctive Queries for Logic-Based Information Extraction

M.¹

2022

Preprint

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This thesis offers two logic-based approaches to conjunctive queries in the context of information extraction. The first and main approach is the introduction of conjunctive query fragments of the logics FC and FC [REG], denoted as FC-CQ and FC[REG]-CQ respectively. FC is a first-order logic based on word equations, where the semantics are defined by limiting the universe to the factors of some finite input word. FC [REG] is FC extended with regular constraints.Our first results consider the comparative expressive power of FC[REG]-CQ in relation to document spanners (a formal framework for the query language AQL), and various fragments of FC[REG]-CQ -some of which coincide with well-known language generators, such as patterns and regular expressions. better supervisor and mentor.I'd also like to thank the numerous people at Loughborough university who have helped me during my time here, both as an undergraduate student and a PhD student. I am grateful to Daniel Reidenbach for being my second supervisor, as well as for sparking my interest in theoretical computer science with his undergraduate module. Thank you to Andrea Soltoggio and Szymon Łopaciuk for all the interesting discussions over lunch. An additional thanks to Szymon for numerous conversations in the office about research and more. I wish to express my gratitude to Parisa Derakhshan, Iain Phillips, Robert Mercaş, Manfred Kufleitner, Dominik D. Freydenberger, and Yanning Yang for allowing me to teach their modules. Doing so has made me a more well-rounded computer scientist.I am grateful to Joel D. Day and Ana Sălăgean for agreeing to be my internal examiners, and Anthony W. Lin for being my external examiner.I would also like to thank Justin Brackemann for the helpful feedback and list of typos in the proof of Theorem 4.12.Last, but not least, I'd like to thank my family. Without all their encouragement, I would not have been able to finish this project. I can't put into words how thankful I am for my parents, my sister, and my grandparents.v Contents Abstract iiiAcknowledgements v Document Spanners. Document spanners were introduced by Fagin, Kimelfeld, Reiss, and Vansummeren [31] as a formal framework for the Annotation Query Language (or AQL) used in IBM's SystemT. Regarding data complexity, Florenzano, Riveros, Ugarte, Vansummeren, and Vrgoc [34] gave a constant-delay algorithm for enumerating the results of deterministic vset-automata, after linear time preprocessing. Amarilli, Bourhis, Mengal, and Niewerth [3] extended this result to nondeterministic vset-automata.Regarding combined complexity, Freydenberger, Kimelfeld, and Peterfreund [39] introduced regex CQs and proved that their evaluation is NP-complete (even for acyclic queries), and that fixing the number of atoms and the number of equalities in SERCQs allows for polynomial-delay enumeration of results. Freydenberger, Peterfreund, Kimelfeld, and Kröll [89] showed that non-emptiness for a join of two sequential regex formulas is NP-hard, under schemaless semantics, even for a single c...

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Section: Base Case 2 (X ∈ γ) For Every X ∈ Vars (ψ) and Every Regular...mentioning

confidence: 92%

Section: Chapter 5 Dynamic Complexitymentioning

confidence: 99%

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Conjunctive Queries for Logic-Based Information Extraction

M.¹

2022

Preprint

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“…When we use a different initialization setting we state it explicitly. In the literature several other settings have been investigated and we refer to [25,23] for a detailed discussion.…”

Section: Definition 2 (Dynamic Program)mentioning

confidence: 99%

Dynamic Graph Queries

Muñoz,

Vortmeier,

Zeume

2015

Preprint

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Graph databases in many applications-semantic web, transport or biological networks among others-are not only large, but also frequently modified. Evaluating graph queries in this dynamic context is a challenging task, as those queries often combine first-order and navigational features.Motivated by recent results on maintaining dynamic reachability, we study the dynamic evaluation of traditional query languages for graphs in the descriptive complexity framework. Our focus is on maintaining regular path queries, and extensions thereof, by first-order formulas. In particular we are interested in path queries defined by non-regular languages and in extended conjunctive regular path queries (which allow to compare labels of paths based on word relations). Further we study the closely related problems of maintaining distances in graphs and reachability in product graphs.In this preliminary study we obtain upper bounds for those problems in restricted settings, such as undirected and acyclic graphs, or under insertions only, and negative results regarding quantifier-free update formulas. In addition we point out interesting directions for further research.

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“…Further classes of query languages for labeled graphs have been studied in the dynamic context in the literature, see [42,44,33].…”

Section: Corollary 9 Regular Path Queries and Conjunctions Thereof Ca...mentioning

confidence: 99%

Reachability is in DynFO

Datta¹,

Kulkarni²,

Mukherjee³

et al. 2015

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Patnaik and Immerman introduced the dynamic complexity classDynFO of database queries that can be maintained by first-order dynamic programs with the help of auxiliary relations under insertions and deletions of edges [34]. This article confirms their conjecture that the Reachability query is in DynFO.As a byproduct it is shown that the rank of a matrix with small values can be maintained in DynFO(+,×). It is further shown that the (size of the) maximum matching of a graph can be maintained in non-uniform DynFO, another extension of DynFO, with non-uniform initialisation of the auxiliary relations.

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Small Dynamic Complexity Classes

Cited by 4 publications

References 50 publications

Conjunctive Queries for Logic-Based Information Extraction

Conjunctive Queries for Logic-Based Information Extraction

Dynamic Graph Queries

Reachability is in DynFO

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