Document

**Published in:** LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

We introduce the 2-sorted counting logic GC^k and its restriction RGC^k that express properties of hypergraphs. These logics have available k variables to address hyperedges, an unbounded number of variables to address vertices of a hypergraph, and atomic formulas E(e,v) to express that a vertex v is contained in a hyperedge e. We show that two hypergraphs H,H' satisfy the same sentences of the logic RGC^k if, and only if, they are homomorphism indistinguishable over the class of hypergraphs of generalised hypertree width at most k. Here, H,H' are called homomorphism indistinguishable over a class 𝒞 if for every hypergraph G ∈ 𝒞 the number of homomorphisms from G to H equals the number of homomorphisms from G to H'. This result can be viewed as a lifting (from graphs to hypergraphs) of a result by Dvořák (2010) stating that any two (undirected, simple, finite) graphs H,H' are indistinguishable by the k+1-variable counting logic C^{k+1} if, and only if, they are homomorphism indistinguishable over the class of graphs of tree-width at most k.

Benjamin Scheidt and Nicole Schweikardt. Counting Homomorphisms from Hypergraphs of Bounded Generalised Hypertree Width: A Logical Characterisation. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 79:1-79:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{scheidt_et_al:LIPIcs.MFCS.2023.79, author = {Scheidt, Benjamin and Schweikardt, Nicole}, title = {{Counting Homomorphisms from Hypergraphs of Bounded Generalised Hypertree Width: A Logical Characterisation}}, booktitle = {48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)}, pages = {79:1--79:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-292-1}, ISSN = {1868-8969}, year = {2023}, volume = {272}, editor = {Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.79}, URN = {urn:nbn:de:0030-drops-186131}, doi = {10.4230/LIPIcs.MFCS.2023.79}, annote = {Keywords: counting logics, guarded logics, homomorphism counting, hypertree decompositions, hypergraphs, incidence graphs, quantum graphs} }

Document

**Published in:** LIPIcs, Volume 220, 25th International Conference on Database Theory (ICDT 2022)

We introduce subsequence-queries with wildcards and gap-size constraints (swg-queries, for short) as a tool for querying event traces. An swg-query q is given by a string s over an alphabet of variables and types, a global window size w, and a tuple c = ((c^-_1, c^+_1), (c^-_2, c^+_2), …, (c^-_{|s|-1}, c^+_{|s|-1})) of local gap-size constraints over ℕ × (ℕ ∪ {∞}). The query q matches in a trace t (i. e., a sequence of types) if the variables can uniformly be substituted by types such that the resulting string occurs in t as a subsequence that spans an area of length at most w, and the i^{th} gap of the subsequence (i. e., the distance between the i^{th} and (i+1)^{th} position of the subsequence) has length at least c^-_i and at most c^+_i. We formalise and investigate the task of discovering an swg-query that describes best the traces from a given sample S of traces, and we present an algorithm solving this task. As a central component, our algorithm repeatedly solves the matching problem (i. e., deciding whether a given query q matches in a given trace t), which is an NP-complete problem (in combined complexity). Hence, the matching problem is of special interest in the context of query discovery, and we therefore subject it to a detailed (parameterised) complexity analysis to identify tractable subclasses, which lead to tractable subclasses of the discovery problem as well. We complement this by a reduction proving that any query discovery algorithm also yields an algorithm for the matching problem. Hence, lower bounds on the complexity of the matching problem directly translate into according lower bounds of the query discovery problem. As a proof of concept, we also implemented a prototype of our algorithm and tested it on real-world data.

Sarah Kleest-Meißner, Rebecca Sattler, Markus L. Schmid, Nicole Schweikardt, and Matthias Weidlich. Discovering Event Queries from Traces: Laying Foundations for Subsequence-Queries with Wildcards and Gap-Size Constraints. In 25th International Conference on Database Theory (ICDT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 220, pp. 18:1-18:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kleestmeiner_et_al:LIPIcs.ICDT.2022.18, author = {Kleest-Mei{\ss}ner, Sarah and Sattler, Rebecca and Schmid, Markus L. and Schweikardt, Nicole and Weidlich, Matthias}, title = {{Discovering Event Queries from Traces: Laying Foundations for Subsequence-Queries with Wildcards and Gap-Size Constraints}}, booktitle = {25th International Conference on Database Theory (ICDT 2022)}, pages = {18:1--18:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-223-5}, ISSN = {1868-8969}, year = {2022}, volume = {220}, editor = {Olteanu, Dan and Vortmeier, Nils}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2022.18}, URN = {urn:nbn:de:0030-drops-158922}, doi = {10.4230/LIPIcs.ICDT.2022.18}, annote = {Keywords: event queries on traces, pattern queries on strings, learning descriptive queries, complexity of query evaluation and query learning} }

Document

**Published in:** LIPIcs, Volume 186, 24th International Conference on Database Theory (ICDT 2021)

The regular spanners (characterised by vset-automata) are closed under the algebraic operations of union, join and projection, and have desirable algorithmic properties. The core spanners (introduced by Fagin, Kimelfeld, Reiss, and Vansummeren (PODS 2013, JACM 2015) as a formalisation of the core functionality of the query language AQL used in IBM’s SystemT) additionally need string equality selections and it has been shown by Freydenberger and Holldack (ICDT 2016, Theory of Computing Systems 2018) that this leads to high complexity and even undecidability of the typical problems in static analysis and query evaluation. We propose an alternative approach to core spanners: by incorporating the string-equality selections directly into the regular language that represents the underlying regular spanner (instead of treating it as an algebraic operation on the table extracted by the regular spanner), we obtain a fragment of core spanners that, while having slightly weaker expressive power than the full class of core spanners, arguably still covers the intuitive applications of string equality selections for information extraction and has much better upper complexity bounds of the typical problems in static analysis and query evaluation.

Markus L. Schmid and Nicole Schweikardt. A Purely Regular Approach to Non-Regular Core Spanners. In 24th International Conference on Database Theory (ICDT 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 186, pp. 4:1-4:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{schmid_et_al:LIPIcs.ICDT.2021.4, author = {Schmid, Markus L. and Schweikardt, Nicole}, title = {{A Purely Regular Approach to Non-Regular Core Spanners}}, booktitle = {24th International Conference on Database Theory (ICDT 2021)}, pages = {4:1--4:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-179-5}, ISSN = {1868-8969}, year = {2021}, volume = {186}, editor = {Yi, Ke and Wei, Zhewei}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2021.4}, URN = {urn:nbn:de:0030-drops-137124}, doi = {10.4230/LIPIcs.ICDT.2021.4}, annote = {Keywords: Document spanners, regular expressions with backreferences} }

Document

**Published in:** LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)

We consider weighted structures, which extend ordinary relational structures by assigning weights, i.e. elements from a particular group or ring, to tuples present in the structure. We introduce an extension of first-order logic that allows to aggregate weights of tuples, compare such aggregates, and use them to build more complex formulas. We provide locality properties of fragments of this logic including Feferman-Vaught decompositions and a Gaifman normal form for a fragment called FOW₁, as well as a localisation theorem for a larger fragment called FOWA₁. This fragment can express concepts from various machine learning scenarios. Using the locality properties, we show that concepts definable in FOWA₁ over a weighted background structure of at most polylogarithmic degree are agnostically PAC-learnable in polylogarithmic time after pseudo-linear time preprocessing.

Steffen van Bergerem and Nicole Schweikardt. Learning Concepts Described By Weight Aggregation Logic. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 10:1-10:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{vanbergerem_et_al:LIPIcs.CSL.2021.10, author = {van Bergerem, Steffen and Schweikardt, Nicole}, title = {{Learning Concepts Described By Weight Aggregation Logic}}, booktitle = {29th EACSL Annual Conference on Computer Science Logic (CSL 2021)}, pages = {10:1--10:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-175-7}, ISSN = {1868-8969}, year = {2021}, volume = {183}, editor = {Baier, Christel and Goubault-Larrecq, Jean}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.10}, URN = {urn:nbn:de:0030-drops-134447}, doi = {10.4230/LIPIcs.CSL.2021.10}, annote = {Keywords: first-order definable concept learning, agnostic probably approximately correct learning, classification problems, locality, Feferman-Vaught decomposition, Gaifman normal form, first-order logic with counting, weight aggregation logic} }

Document

**Published in:** Dagstuhl Reports, Volume 9, Issue 5 (2019)

This report documents the program and the outcomes of Dagstuhl Seminar 19211 "Enumeration in Data Management". The goal of the seminar was to bring together researchers from various fields of computer science, including the Databases, Computational Logic, and Algorithms communities, and establish the means of collaboration towards considerable progress on the topic. Specifically, we aimed at understanding the recent developments, identifying the important open problems, and initiating collaborative efforts towards solutions thereof. In addition, we aimed to build and disseminate a toolkit for data-centric enumeration problems, including algorithmic techniques, proof techniques, and important indicator problems. Towards the objectives, the seminar included tutorials on the topic, invited talks, presentations of open problems, working groups on the open problems, discussions on platforms to compile the community knowledge, and the construction of various skeletons of such compilations.

Endre Boros, Benny Kimelfeld, Reinhard Pichler, and Nicole Schweikardt. Enumeration in Data Management (Dagstuhl Seminar 19211). In Dagstuhl Reports, Volume 9, Issue 5, pp. 89-109, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@Article{boros_et_al:DagRep.9.5.89, author = {Boros, Endre and Kimelfeld, Benny and Pichler, Reinhard and Schweikardt, Nicole}, title = {{Enumeration in Data Management (Dagstuhl Seminar 19211)}}, pages = {89--109}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2019}, volume = {9}, number = {5}, editor = {Boros, Endre and Kimelfeld, Benny and Pichler, Reinhard and Schweikardt, Nicole}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagRep.9.5.89}, URN = {urn:nbn:de:0030-drops-113822}, doi = {10.4230/DagRep.9.5.89}, annote = {Keywords: constant delay, databases, dynamic complexity, enumeration, polynomial delay, query evaluation} }

Document

**Published in:** LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Marx (STOC 2010, J. ACM 2013) introduced the notion of submodular width of a conjunctive query (CQ) and showed that for any class Phi of Boolean CQs of bounded submodular width, the model-checking problem for Phi on the class of all finite structures is fixed-parameter tractable (FPT). Note that for non-Boolean queries, the size of the query result may be far too large to be computed entirely within FPT time. We investigate the free-connex variant of submodular width and generalise Marx’s result to non-Boolean queries as follows: For every class Phi of CQs of bounded free-connex submodular width, within FPT-preprocessing time we can build a data structure that allows to enumerate, without repetition and with constant delay, all tuples of the query result. Our proof builds upon Marx’s splitting routine to decompose the query result into a union of results; but we have to tackle the additional technical difficulty to ensure that these can be enumerated efficiently.

Christoph Berkholz and Nicole Schweikardt. Constant Delay Enumeration with FPT-Preprocessing for Conjunctive Queries of Bounded Submodular Width. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 58:1-58:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{berkholz_et_al:LIPIcs.MFCS.2019.58, author = {Berkholz, Christoph and Schweikardt, Nicole}, title = {{Constant Delay Enumeration with FPT-Preprocessing for Conjunctive Queries of Bounded Submodular Width}}, booktitle = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)}, pages = {58:1--58:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-117-7}, ISSN = {1868-8969}, year = {2019}, volume = {138}, editor = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.58}, URN = {urn:nbn:de:0030-drops-110021}, doi = {10.4230/LIPIcs.MFCS.2019.58}, annote = {Keywords: conjunctive queries, constant delay enumeration, hypertree decompositions, submodular width, fixed-parameter tractability} }

Document

**Published in:** LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

We consider the extension of first-order logic FO by unary counting quantifiers and generalise the notion of Gaifman normal form from FO to this setting. For formulas that use only ultimately periodic counting quantifiers, we provide an algorithm that computes equivalent formulas in Gaifman normal form. We also show that this is not possible for formulas using at least one quantifier that is not ultimately periodic.
Now let d be a degree bound. We show that for any formula phi with arbitrary counting quantifiers, there is a formula gamma in Gaifman normal form that is equivalent to phi on all finite structures of degree <= d. If the quantifiers of phi are decidable (decidable in elementary time, ultimately periodic), gamma can be constructed effectively (in elementary time, in worst-case optimal 3-fold exponential time).
For the setting with unrestricted degree we show that by using our Gaifman normal form for formulas with only ultimately periodic counting quantifiers, a known fixed-parameter tractability result for FO on classes of structures of bounded local tree-width can be lifted to the extension of FO with ultimately periodic counting quantifiers (a logic equally expressive as FO+MOD, i.e., first-oder logic with modulo-counting quantifiers).

Dietrich Kuske and Nicole Schweikardt. Gaifman Normal Forms for Counting Extensions of First-Order Logic. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 133:1-133:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kuske_et_al:LIPIcs.ICALP.2018.133, author = {Kuske, Dietrich and Schweikardt, Nicole}, title = {{Gaifman Normal Forms for Counting Extensions of First-Order Logic}}, booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, pages = {133:1--133:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-076-7}, ISSN = {1868-8969}, year = {2018}, volume = {107}, editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.133}, URN = {urn:nbn:de:0030-drops-91375}, doi = {10.4230/LIPIcs.ICALP.2018.133}, annote = {Keywords: Finite model theory, Gaifman locality, modulo-counting quantifiers, fixed parameter tractable model-checking} }

Document

**Published in:** LIPIcs, Volume 98, 21st International Conference on Database Theory (ICDT 2018)

We investigate the query evaluation problem for fixed queries over
fully dynamic databases where tuples can be inserted or deleted.
The task is to design a dynamic data structure that can immediately
report the new result of a fixed query after every database update.
We consider unions of conjunctive queries (UCQs) and focus on the query evaluation tasks testing (decide whether an input tuple belongs to the query result), enumeration (enumerate, without repetition,
all tuples in the query result), and counting (output the number of tuples in the query result).
We identify three increasingly restrictive classes of UCQs which we
call t-hierarchical, q-hierarchical, and exhaustively q-hierarchical UCQs.
Our main results provide the following dichotomies:
If the query's homomorphic core is t-hierarchical (q-hierarchical,
exhaustively q-hierarchical), then the testing (enumeration, counting)
problem can be solved with constant update time and constant testing time (delay, counting time). Otherwise, it cannot be solved with sublinear update time and sublinear testing time (delay, counting time), unless the OV-conjecture and/or the OMv-conjecture fails.
We also study the complexity of query evaluation in the dynamic setting in the presence of integrity constraints, and we obtain similar dichotomy results for the special case of small domain constraints (i.e., constraints which state that
all values in a particular column of a relation belong to a fixed domain of constant size).

Christoph Berkholz, Jens Keppeler, and Nicole Schweikardt. Answering UCQs under Updates and in the Presence of Integrity Constraints. In 21st International Conference on Database Theory (ICDT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 98, pp. 8:1-8:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{berkholz_et_al:LIPIcs.ICDT.2018.8, author = {Berkholz, Christoph and Keppeler, Jens and Schweikardt, Nicole}, title = {{Answering UCQs under Updates and in the Presence of Integrity Constraints}}, booktitle = {21st International Conference on Database Theory (ICDT 2018)}, pages = {8:1--8:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-063-7}, ISSN = {1868-8969}, year = {2018}, volume = {98}, editor = {Kimelfeld, Benny and Amsterdamer, Yael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2018.8}, URN = {urn:nbn:de:0030-drops-85990}, doi = {10.4230/LIPIcs.ICDT.2018.8}, annote = {Keywords: dynamic query evaluation, union of conjunctive queries, constant-delay enumeration, counting problem, testing} }

Document

**Published in:** LIPIcs, Volume 68, 20th International Conference on Database Theory (ICDT 2017)

We investigate the query evaluation problem for fixed queries over fully dynamic databases, where tuples can be inserted or deleted. The task is to design a dynamic algorithm that immediately reports the new result of a fixed query after every database update.
We consider queries in first-order logic (FO) and its extension with modulo-counting quantifiers (FO+MOD), and show that they can be efficiently evaluated under updates, provided that the dynamic database does not exceed a certain degree bound.
In particular, we construct a data structure that allows to answer a Boolean FO+MOD query and to compute the size of the query result within constant time after every database update. Furthermore, after every update we are able to immediately enumerate the new query result with constant delay between the output tuples. The time needed to build the data structure is linear in the size of the database.
Our results extend earlier work on the evaluation of first-order queries on static databases of bounded degree and rely on an effective Hanf normal form for FO+MOD recently obtained by [Heimberg, Kuske, and Schweikardt, LICS, 2016].

Christoph Berkholz, Jens Keppeler, and Nicole Schweikardt. Answering FO+MOD Queries Under Updates on Bounded Degree Databases. In 20th International Conference on Database Theory (ICDT 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 68, pp. 8:1-8:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{berkholz_et_al:LIPIcs.ICDT.2017.8, author = {Berkholz, Christoph and Keppeler, Jens and Schweikardt, Nicole}, title = {{Answering FO+MOD Queries Under Updates on Bounded Degree Databases}}, booktitle = {20th International Conference on Database Theory (ICDT 2017)}, pages = {8:1--8:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-024-8}, ISSN = {1868-8969}, year = {2017}, volume = {68}, editor = {Benedikt, Michael and Orsi, Giorgio}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2017.8}, URN = {urn:nbn:de:0030-drops-70535}, doi = {10.4230/LIPIcs.ICDT.2017.8}, annote = {Keywords: dynamic databases, query enumeration, counting problem, first-order logic with modulo-counting quantifiers, Hanf locality} }

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Invited Talk

**Published in:** LIPIcs, Volume 31, 18th International Conference on Database Theory (ICDT 2015)

In the database theory and logic literature, different notions of locality of queries have been studied, the most prominent being Hanf locality and Gaifman locality. These notions are designed so that, in order to evaluate a local query in a given database, it suffices to look only at small neighbourhoods around tuples of elements that belong to the database.
In this talk I want to give a survey of how to use locality for efficient query evaluation in various computation models. In particular, we will take a closer look at how to enumerate query results with constant delay, and at how to evaluate queries in a map-reduce like setting [Neven et al., ICDT 2015] or in Pregel [Malewicz et al., SIGMOD 2010]. Also, we will have a closer look at how to transform a given local query into a form suitable for exploiting its locality.

Nicole Schweikardt. Using Locality for Efficient Query Evaluation in Various Computation Models (Invited Talk). In 18th International Conference on Database Theory (ICDT 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 31, pp. 13-14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)

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@InProceedings{schweikardt:LIPIcs.ICDT.2015.13, author = {Schweikardt, Nicole}, title = {{Using Locality for Efficient Query Evaluation in Various Computation Models}}, booktitle = {18th International Conference on Database Theory (ICDT 2015)}, pages = {13--14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-79-8}, ISSN = {1868-8969}, year = {2015}, volume = {31}, editor = {Arenas, Marcelo and Ugarte, Mart{\'\i}n}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2015.13}, URN = {urn:nbn:de:0030-drops-49987}, doi = {10.4230/LIPIcs.ICDT.2015.13}, annote = {Keywords: query evaluation, locality} }

Document

**Published in:** LIPIcs, Volume 31, 18th International Conference on Database Theory (ICDT 2015)

We introduce three formal models of distributed systems for query evaluation on massive databases: Distributed Streaming with Register Automata (DSAs), Distributed Streaming with Register Transducers (DSTs), and Distributed Streaming with Register Transducers and Joins (DSTJs). These models are based on the key-value paradigm where the input is transformed into a dataset of key-value pairs, and on each key a local computation is performed on the values associated with that key resulting in another set of key-value pairs. Computation proceeds in a constant number of rounds, where the result of the last round is the input to the next round, and transformation to key-value pairs is required to be generic. The difference between the three models is in the local computation part. In DSAs it is limited to making one pass over its input using a register automaton, while in DSTs it can make two passes: in the first pass it uses a finite-state automaton and in the second it uses a register transducer. The third model DSTJs is an extension of DSTs, where local computations are capable of constructing the Cartesian product of two sets. We obtain the following results: (1) DSAs can evaluate first-order queries over bounded degree databases; (2) DSTs can evaluate semijoin algebra queries over arbitrary databases; (3) DSTJs can evaluate the whole relational algebra over arbitrary databases; (4) DSTJs are strictly stronger than DSTs, which in turn, are strictly stronger than DSAs; (5) within DSAs, DSTs and DSTJs there is a strict hierarchy w.r.t. the number of rounds.

Frank Neven, Nicole Schweikardt, Frédéric Servais, and Tony Tan. Distributed Streaming with Finite Memory. In 18th International Conference on Database Theory (ICDT 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 31, pp. 324-341, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)

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@InProceedings{neven_et_al:LIPIcs.ICDT.2015.324, author = {Neven, Frank and Schweikardt, Nicole and Servais, Fr\'{e}d\'{e}ric and Tan, Tony}, title = {{Distributed Streaming with Finite Memory}}, booktitle = {18th International Conference on Database Theory (ICDT 2015)}, pages = {324--341}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-79-8}, ISSN = {1868-8969}, year = {2015}, volume = {31}, editor = {Arenas, Marcelo and Ugarte, Mart{\'\i}n}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2015.324}, URN = {urn:nbn:de:0030-drops-49939}, doi = {10.4230/LIPIcs.ICDT.2015.324}, annote = {Keywords: distributed systems, relational algebra, semijoin algebra, register automata, register transducers.} }

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Complete Volume

**Published in:** Dagstuhl Follow-Ups, Volume 5, Data Exchange, Integration, and Streams (2013)

DFU, Volume 5, Data Exchange, Information, and Streams, Complete Volume

Phokion G. Kolaitis, Maurizio Lenzerini, and Nicole Schweikardt. DFU, Volume 5, Data Exchange, Integration, and Streams, Complete Volume. In Data Exchange, Integration, and Streams. Dagstuhl Follow-Ups, Volume 5, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)

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@Collection{DFU.Vol5.10452, title = {{DFU, Volume 5, Data Exchange, Integration, and Streams, Complete Volume}}, booktitle = {Data Exchange, Integration, and Streams}, series = {Dagstuhl Follow-Ups}, ISBN = {978-3-939897-61-3}, ISSN = {1868-8977}, year = {2013}, volume = {5}, editor = {Kolaitis, Phokion G. and Lenzerini, Maurizio and Schweikardt, Nicole}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DFU.Vol5.10452}, URN = {urn:nbn:de:0030-drops-43032}, doi = {10.4230/DFU.Vol5.10452}, annote = {Keywords: Heterogeneous Databases, Systems, Database Applications, Nonnumerical Algorithms and Problems} }

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**Published in:** Dagstuhl Follow-Ups, Volume 5, Data Exchange, Integration, and Streams (2013)

Frontmatter, Table of Contents, Preface

Phokion G. Kolaitis, Maurizio Lenzerini, and Nicole Schweikardt. Frontmatter, Table of Contents, Preface. In Data Exchange, Integration, and Streams. Dagstuhl Follow-Ups, Volume 5, pp. 0:i-0:x, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)

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@InCollection{kolaitis_et_al:DFU.Vol5.10452.i, author = {Kolaitis, Phokion G. and Lenzerini, Maurizio and Schweikardt, Nicole}, title = {{Frontmatter, Table of Contents, Preface}}, booktitle = {Data Exchange, Integration, and Streams}, pages = {0:i--0:x}, series = {Dagstuhl Follow-Ups}, ISBN = {978-3-939897-61-3}, ISSN = {1868-8977}, year = {2013}, volume = {5}, editor = {Kolaitis, Phokion G. and Lenzerini, Maurizio and Schweikardt, Nicole}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DFU.Vol5.10452.i}, URN = {urn:nbn:de:0030-drops-42875}, doi = {10.4230/DFU.Vol5.10452.i}, annote = {Keywords: Frontmatter, Table of Contents, Preface} }

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**Published in:** LIPIcs, Volume 23, Computer Science Logic 2013 (CSL 2013)

We study Gaifman and Hanf locality of an extension of first-order logic with modulo p counting quantifiers (FO+MODp, for short) with arbitrary numerical predicates. We require that the validity of formulas is independent of the particular interpretation of the numerical predicates and refer to such formulas as arb-invariant formulas. This paper gives a detailed picture of locality and non-locality properties of arb-invariant FO+MODp. For example, on the class of all finite structures, for any p >= 2, arb-invariant FO+MODp is neither Hanf nor Gaifman local with respect to a sublinear locality radius. However, in case that p is an odd prime power, it is weakly Gaifman local with a polylogarithmic locality radius. And when restricting attention to the class of string structures, for odd prime powers p, arb-invariant FO+MODp is both Hanf and Gaifman local with a polylogarithmic locality radius. Our negative results build on examples of order-invariant FO+MODp formulas presented in Niemistö's PhD thesis. Our positive results make use of the close connection between FO+MODp and Boolean circuits built from NOT-gates and AND-, OR-, and MODp-gates of arbitrary fan-in.

Frederik Harwath and Nicole Schweikardt. On the locality of arb-invariant first-order logic with modulo counting quantifiers. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 363-379, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)

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@InProceedings{harwath_et_al:LIPIcs.CSL.2013.363, author = {Harwath, Frederik and Schweikardt, Nicole}, title = {{On the locality of arb-invariant first-order logic with modulo counting quantifiers}}, booktitle = {Computer Science Logic 2013 (CSL 2013)}, pages = {363--379}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-60-6}, ISSN = {1868-8969}, year = {2013}, volume = {23}, editor = {Ronchi Della Rocca, Simona}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.363}, URN = {urn:nbn:de:0030-drops-42086}, doi = {10.4230/LIPIcs.CSL.2013.363}, annote = {Keywords: finite model theory, Gaifman and Hanf locality, first-order logic with modulo counting quantifiers, order-invariant and arb-invariant formulas, lower} }

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**Published in:** LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)

This paper considers the logic FOcard, i.e., first-order logic with cardinality predicates that can specify the size of a structure modulo some number. We study the expressive power of FOcard on the class of languages of ranked, finite, labelled trees with successor relations.
Our first main result characterises the class of FOcard-definable tree
languages in terms of algebraic closure properties of the tree languages. As it can be effectively checked whether the language of a given tree automaton satisfies these closure properties, we obtain a
decidable characterisation of the class of regular tree languages definable in FOcard.
Our second main result considers first-order logic with unary relations, successor relations, and two additional designated symbols < and + that must be interpreted as a linear order and its associated addition. Such a formula is called addition-invariant if, for each fixed interpretation of the unary relations and successor relations, its result is independent of the particular interpretation of < and +.
We show that the FOcard-definable tree languages are exactly the regular tree languages definable in addition-invariant first-order logic.
Our proof techniques involve tools from algebraic automata theory,
reasoning with locality arguments, and the use of logical interpretations. We combine and extend methods developed by Benedikt and Segoufin (ACM ToCL, 2009) and Schweikardt and Segoufin (LICS, 2010).

Frederik Harwath and Nicole Schweikardt. Regular tree languages, cardinality predicates, and addition-invariant FO. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 489-500, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)

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@InProceedings{harwath_et_al:LIPIcs.STACS.2012.489, author = {Harwath, Frederik and Schweikardt, Nicole}, title = {{Regular tree languages, cardinality predicates, and addition-invariant FO}}, booktitle = {29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)}, pages = {489--500}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-35-4}, ISSN = {1868-8969}, year = {2012}, volume = {14}, editor = {D\"{u}rr, Christoph and Wilke, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.489}, URN = {urn:nbn:de:0030-drops-34394}, doi = {10.4230/LIPIcs.STACS.2012.489}, annote = {Keywords: regular tree languages, algebraic closure properties, decidable characterisations, addition-invariant first-order logic, logical interpretations} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 10501, Advances and Applications of Automata on Words and Trees (2011)

From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501
``Advances and Applications of Automata on Words and Trees'' was held
in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.

Christian Glasser, Jean-Eric Pin, Nicole Schweikardt, Victor Selivanov, and Wolfgang Thomas. 10501 Abstracts Collection – Advances and Applications of Automata on Words and Trees. In Advances and Applications of Automata on Words and Trees. Dagstuhl Seminar Proceedings, Volume 10501, pp. 1-12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)

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@InProceedings{glasser_et_al:DagSemProc.10501.1, author = {Glasser, Christian and Pin, Jean-Eric and Schweikardt, Nicole and Selivanov, Victor and Thomas, Wolfgang}, title = {{10501 Abstracts Collection – Advances and Applications of Automata on Words and Trees}}, booktitle = {Advances and Applications of Automata on Words and Trees}, pages = {1--12}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2011}, volume = {10501}, editor = {Christian Glasser and Jean-Eric Pin and Nicole Schweikardt and Victor Selivanov and Wolfgang Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10501.1}, URN = {urn:nbn:de:0030-drops-31486}, doi = {10.4230/DagSemProc.10501.1}, annote = {Keywords: Automata theory, logic, verification, data structures, algorithms, complexity, games, infinite games with perfect information, reactive systems, specification and verification, combinatorics, hierarchies and reducibilities} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 10501, Advances and Applications of Automata on Words and Trees (2011)

The aim of the seminar was to discuss and systematize
the recent fast progress in automata theory and to identify
important directions for future research.
For this, the seminar brought together more than 40 researchers
from automata theory and related fields of applications.
We had 19 talks of 30 minutes and 5 one-hour lectures
leaving ample room for discussions.
In the following we describe the topics in more detail.

Christian Glasser, Jean-Eric Pin, Nicole Schweikardt, Victor Selivanov, and Wolfgang Thomas. 10501 Executive Summary – Advances and Applications of Automata on Words and Trees. In Advances and Applications of Automata on Words and Trees. Dagstuhl Seminar Proceedings, Volume 10501, pp. 1-4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)

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@InProceedings{glasser_et_al:DagSemProc.10501.2, author = {Glasser, Christian and Pin, Jean-Eric and Schweikardt, Nicole and Selivanov, Victor and Thomas, Wolfgang}, title = {{10501 Executive Summary – Advances and Applications of Automata on Words and Trees}}, booktitle = {Advances and Applications of Automata on Words and Trees}, pages = {1--4}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2011}, volume = {10501}, editor = {Christian Glasser and Jean-Eric Pin and Nicole Schweikardt and Victor Selivanov and Wolfgang Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10501.2}, URN = {urn:nbn:de:0030-drops-31474}, doi = {10.4230/DagSemProc.10501.2}, annote = {Keywords: Infinite games with perfect information, reactive systems, specification and verification, combinatorics, hierarchies and reducibilities} }

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**Published in:** LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)

This paper gives a brief overview of computation models for data stream processing, and it introduces a new model for multi-pass processing of multiple streams, the so-called \emph{mp2s-automata}. Two algorithms for solving the set disjointness problem with these automata are presented. The main technical contribution of this paper is the proof of a lower bound on the size of memory and the number of heads that are required for solving the set disjointness problem with mp2s-automata.

Nicole Schweikardt. Lower Bounds for Multi-Pass Processing of Multiple Data Streams. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 51-62, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)

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@InProceedings{schweikardt:LIPIcs.STACS.2009.1857, author = {Schweikardt, Nicole}, title = {{Lower Bounds for Multi-Pass Processing of Multiple Data Streams}}, booktitle = {26th International Symposium on Theoretical Aspects of Computer Science}, pages = {51--62}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-09-5}, ISSN = {1868-8969}, year = {2009}, volume = {3}, editor = {Albers, Susanne and Marion, Jean-Yves}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1857}, URN = {urn:nbn:de:0030-drops-18575}, doi = {10.4230/LIPIcs.STACS.2009.1857}, annote = {Keywords: Data streams, Lower bounds, Machine models, Automata, The set disjointness problem} }

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