43 Search Results for "Zeume, Thomas"

Volume

LIPIcs, Volume 48

19th International Conference on Database Theory (ICDT 2016)

ICDT 2016, March 15-18, 2016, Bordeaux, France

Editors: Wim Martens and Thomas Zeume

Document
DOI: 10.4230/LIPIcs.CONCUR.2023.29
Constraint Automata on Infinite Data Trees: from CTL(ℤ)/CTL^*(ℤ) to Decision Procedures

Authors: Stéphane Demri and Karin Quaas

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract
We introduce the class of tree constraint automata with data values in ℤ (equipped with the less than relation and equality predicates to constants), and we show that the nonemptiness problem is EXPTIME-complete. Using an automata-based approach, we establish that the satisfiability problem for CTL(ℤ) (CTL with constraints in ℤ) is EXPTIME-complete, and the satisfiability problem for CTL^*(ℤ) is 2ExpTime-complete (only decidability was known so far). By-product results with other concrete domains and other logics, are also briefly discussed.
Cite as

Stéphane Demri and Karin Quaas. Constraint Automata on Infinite Data Trees: from CTL(ℤ)/CTL^*(ℤ) to Decision Procedures. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 29:1-29:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{demri_et_al:LIPIcs.CONCUR.2023.29,
  author =	{Demri, St\'{e}phane and Quaas, Karin},
  title =	{{Constraint Automata on Infinite Data Trees: from CTL(\mathbb{Z})/CTL^*(\mathbb{Z}) to Decision Procedures}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.29},
  URN =		{urn:nbn:de:0030-drops-190238},
  doi =		{10.4230/LIPIcs.CONCUR.2023.29},
  annote =	{Keywords: Constraints, Constraint Automata, Temporal Logics, Infinite Data Trees}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.39
Dynamic Planar Embedding Is in DynFO

Authors: Samir Datta, Asif Khan, and Anish Mukherjee

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

Abstract
Planar Embedding is a drawing of a graph on the plane such that the edges do not intersect each other except at the vertices. We know that testing the planarity of a graph and computing its embedding (if it exists), can efficiently be computed, both sequentially [John E. Hopcroft and Robert Endre Tarjan, 1974] and in parallel [Vijaya Ramachandran and John H. Reif, 1994], when the entire graph is presented as input. In the dynamic setting, the input graph changes one edge at a time through insertion and deletions and planarity testing/embedding has to be updated after every change. By storing auxilliary information we can improve the complexity of dynamic planarity testing/embedding over the obvious recomputation from scratch. In the sequential dynamic setting, there has been a series of works [David Eppstein et al., 1996; Giuseppe F. Italiano et al., 1993; Jacob Holm et al., 2018; Jacob Holm and Eva Rotenberg, 2020], culminating in the breakthrough result of polylog(n) sequential time (amortized) planarity testing algorithm of Holm and Rotenberg [Jacob Holm and Eva Rotenberg, 2020]. In this paper we study planar embedding through the lens of DynFO, a parallel dynamic complexity class introduced by Patnaik et al [Sushant Patnaik and Neil Immerman, 1997] (also [Guozhu Dong et al., 1995]). We show that it is possible to dynamically maintain whether an edge can be inserted to a planar graph without causing non-planarity in DynFO. We extend this to show how to maintain an embedding of a planar graph under both edge insertions and deletions, while rejecting edge insertions that violate planarity. Our main idea is to maintain embeddings of only the triconnected components and a special two-colouring of separating pairs that enables us to side-step cascading flips when embedding of a biconnected planar graph changes, a major issue for sequential dynamic algorithms [Jacob Holm and Eva Rotenberg, 2020; Jacob Holm and Eva Rotenberg, 2020].
Cite as

Samir Datta, Asif Khan, and Anish Mukherjee. Dynamic Planar Embedding Is in DynFO. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 39:1-39:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{datta_et_al:LIPIcs.MFCS.2023.39,
  author =	{Datta, Samir and Khan, Asif and Mukherjee, Anish},
  title =	{{Dynamic Planar Embedding Is in DynFO}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{39:1--39:15},
  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.2023.39},
  URN =		{urn:nbn:de:0030-drops-185736},
  doi =		{10.4230/LIPIcs.MFCS.2023.39},
  annote =	{Keywords: Dynamic Complexity, Planar graphs, Planar embedding}
}
Document
DOI: 10.4230/LIPIcs.CSL.2023.35
Dynamic Complexity of Regular Languages: Big Changes, Small Work

Authors: Felix Tschirbs, Nils Vortmeier, and Thomas Zeume

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract
Whether a changing string is member of a certain regular language can be maintained in the DynFO framework of Patnaik and Immerman: after changing the symbol at one position of the string, a first-order update formula can express - using additionally stored information - whether the resulting string is in the regular language. We extend this and further known results by considering changes of many positions at once. We also investigate to which degree the obtained update formulas imply work-efficient parallel dynamic algorithms.
Cite as

Felix Tschirbs, Nils Vortmeier, and Thomas Zeume. Dynamic Complexity of Regular Languages: Big Changes, Small Work. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 35:1-35:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{tschirbs_et_al:LIPIcs.CSL.2023.35,
  author =	{Tschirbs, Felix and Vortmeier, Nils and Zeume, Thomas},
  title =	{{Dynamic Complexity of Regular Languages: Big Changes, Small Work}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{35:1--35:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.35},
  URN =		{urn:nbn:de:0030-drops-174963},
  doi =		{10.4230/LIPIcs.CSL.2023.35},
  annote =	{Keywords: dynamic descriptive complexity, regular languages, batch changes, work}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2022.118
Dynamic Meta-Theorems for Distance and Matching

Authors: Samir Datta, Chetan Gupta, Rahul Jain, Anish Mukherjee, Vimal Raj Sharma, and Raghunath Tewari

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
Reachability, distance, and matching are some of the most fundamental graph problems that have been of particular interest in dynamic complexity theory in recent years [Samir Datta et al., 2018; Samir Datta et al., 2018; Samir Datta et al., 2020]. Reachability can be maintained with first-order update formulas, or equivalently in DynFO in general graphs with n nodes [Samir Datta et al., 2018], even under O(log(n)/log log(n)) changes per step [Samir Datta et al., 2018]. In the context of how large the number of changes can be handled, it has recently been shown [Samir Datta et al., 2020] that under a polylogarithmic number of changes, reachability is in DynFOpar in planar, bounded treewidth, and related graph classes - in fact in any graph where small non-zero circulation weights can be computed in NC. We continue this line of investigation and extend the meta-theorem for reachability to distance and bipartite maximum matching with the same bounds. These are amongst the most general classes of graphs known where we can maintain these problems deterministically without using a majority quantifier and even maintain witnesses. For the bipartite matching result, modifying the approach from [Stephen A. Fenner et al., 2016], we convert the static non-zero circulation weights to dynamic matching-isolating weights. While reachability is in DynFOar under O(log(n)/log log(n)) changes, no such bound is known for either distance or matching in any non-trivial class of graphs under non-constant changes. We show that, in the same classes of graphs as before, bipartite maximum matching is in DynFOar under O(log(n)/log log(n)) changes per step. En route to showing this we prove that the rank of a matrix can be maintained in DynFOar, also under O(log(n)/log log(n)) entry changes, improving upon the previous O(1) bound [Samir Datta et al., 2018]. This implies a similar extension for the non-uniform DynFO bound for maximum matching in general graphs and an alternate algorithm for maintaining reachability under O(log(n)/log log(n)) changes [Samir Datta et al., 2018].
Cite as

Samir Datta, Chetan Gupta, Rahul Jain, Anish Mukherjee, Vimal Raj Sharma, and Raghunath Tewari. Dynamic Meta-Theorems for Distance and Matching. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 118:1-118:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{datta_et_al:LIPIcs.ICALP.2022.118,
  author =	{Datta, Samir and Gupta, Chetan and Jain, Rahul and Mukherjee, Anish and Sharma, Vimal Raj and Tewari, Raghunath},
  title =	{{Dynamic Meta-Theorems for Distance and Matching}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{118:1--118:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.118},
  URN =		{urn:nbn:de:0030-drops-164598},
  doi =		{10.4230/LIPIcs.ICALP.2022.118},
  annote =	{Keywords: Dynamic Complexity, Distance, Matching, Derandomization, Isolation, Matrix Rank}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2020.122
Dynamic Complexity of Reachability: How Many Changes Can We Handle?

Authors: Samir Datta, Pankaj Kumar, Anish Mukherjee, Anuj Tawari, Nils Vortmeier, and Thomas Zeume

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
In 2015, it was shown that reachability for arbitrary directed graphs can be updated by first-order formulas after inserting or deleting single edges. Later, in 2018, this was extended for changes of size (log n)/(log log n), where n is the size of the graph. Changes of polylogarithmic size can be handled when also majority quantifiers may be used. In this paper we extend these results by showing that, for changes of polylogarithmic size, first-order update formulas suffice for maintaining (1) undirected reachability, and (2) directed reachability under insertions. For classes of directed graphs for which efficient parallel algorithms can compute non-zero circulation weights, reachability can be maintained with update formulas that may use "modulo 2" quantifiers under changes of polylogarithmic size. Examples for these classes include the class of planar graphs and graphs with bounded treewidth. The latter is shown here. As the logics we consider cannot maintain reachability under changes of larger sizes, our results are optimal with respect to the size of the changes.
Cite as

Samir Datta, Pankaj Kumar, Anish Mukherjee, Anuj Tawari, Nils Vortmeier, and Thomas Zeume. Dynamic Complexity of Reachability: How Many Changes Can We Handle?. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 122:1-122:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{datta_et_al:LIPIcs.ICALP.2020.122,
  author =	{Datta, Samir and Kumar, Pankaj and Mukherjee, Anish and Tawari, Anuj and Vortmeier, Nils and Zeume, Thomas},
  title =	{{Dynamic Complexity of Reachability: How Many Changes Can We Handle?}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{122:1--122:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.122},
  URN =		{urn:nbn:de:0030-drops-125291},
  doi =		{10.4230/LIPIcs.ICALP.2020.122},
  annote =	{Keywords: Dynamic complexity, reachability, complex changes}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2020.11
Dynamic Complexity of Document Spanners

Authors: Dominik D. Freydenberger and Sam M. Thompson

Published in: LIPIcs, Volume 155, 23rd International Conference on Database Theory (ICDT 2020)

Abstract
The present paper investigates the dynamic complexity of document spanners, a formal framework for information extraction introduced by Fagin, Kimelfeld, Reiss, and Vansummeren (JACM 2015). We first look at the class of regular spanners and prove that any regular spanner can be maintained in the dynamic complexity class DynPROP. This result follows from work done previously on the dynamic complexity of formal languages by Gelade, Marquardt, and Schwentick (TOCL 2012). To investigate core spanners we use SpLog, a concatenation logic that exactly captures core spanners. We show that the dynamic complexity class DynCQ is more expressive than SpLog and therefore can maintain any core spanner. This result is then extended to show that DynFO can maintain any generalized core spanner and that DynFO is more powerful than SpLog with negation.
Cite as

Dominik D. Freydenberger and Sam M. Thompson. Dynamic Complexity of Document Spanners. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 11:1-11:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{freydenberger_et_al:LIPIcs.ICDT.2020.11,
  author =	{Freydenberger, Dominik D. and Thompson, Sam M.},
  title =	{{Dynamic Complexity of Document Spanners}},
  booktitle =	{23rd International Conference on Database Theory (ICDT 2020)},
  pages =	{11:1--11:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-139-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{155},
  editor =	{Lutz, Carsten and Jung, Jean Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2020.11},
  URN =		{urn:nbn:de:0030-drops-119355},
  doi =		{10.4230/LIPIcs.ICDT.2020.11},
  annote =	{Keywords: Document spanners, information extraction, dynamic complexity, descriptive complexity, word equations}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2020.13
Distribution Constraints: The Chase for Distributed Data

Authors: Gaetano Geck, Frank Neven, and Thomas Schwentick

Published in: LIPIcs, Volume 155, 23rd International Conference on Database Theory (ICDT 2020)

Abstract
This paper introduces a declarative framework to specify and reason about distributions of data over computing nodes in a distributed setting. More specifically, it proposes distribution constraints which are tuple and equality generating dependencies (tgds and egds) extended with node variables ranging over computing nodes. In particular, they can express co-partitioning constraints and constraints about range-based data distributions by using comparison atoms. The main technical contribution is the study of the implication problem of distribution constraints. While implication is undecidable in general, relevant fragments of so-called data-full constraints are exhibited for which the corresponding implication problems are complete for EXPTIME, PSPACE and NP. These results yield bounds on deciding parallel-correctness for conjunctive queries in the presence of distribution constraints.
Cite as

Gaetano Geck, Frank Neven, and Thomas Schwentick. Distribution Constraints: The Chase for Distributed Data. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 13:1-13:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{geck_et_al:LIPIcs.ICDT.2020.13,
  author =	{Geck, Gaetano and Neven, Frank and Schwentick, Thomas},
  title =	{{Distribution Constraints: The Chase for Distributed Data}},
  booktitle =	{23rd International Conference on Database Theory (ICDT 2020)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-139-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{155},
  editor =	{Lutz, Carsten and Jung, Jean Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2020.13},
  URN =		{urn:nbn:de:0030-drops-119378},
  doi =		{10.4230/LIPIcs.ICDT.2020.13},
  annote =	{Keywords: tuple-generating dependencies, chase, conjunctive queries, distributed evaluation}
}
Document
DOI: 10.4230/LIPIcs.CSL.2020.36
Dynamic Complexity Meets Parameterised Algorithms

Authors: Jonas Schmidt, Thomas Schwentick, Nils Vortmeier, Thomas Zeume, and Ioannis Kokkinis

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)

Abstract
Dynamic Complexity studies the maintainability of queries with logical formulas in a setting where the underlying structure or database changes over time. Most often, these formulas are from first-order logic, giving rise to the dynamic complexity class DynFO. This paper investigates extensions of DynFO in the spirit of parameterised algorithms. In this setting structures come with a parameter k and the extensions allow additional "space" of size f(k) (in the form of an additional structure of this size) or additional time f(k) (in the form of iterations of formulas) or both. The resulting classes are compared with their non-dynamic counterparts and other classes. The main part of the paper explores the applicability of methods for parameterised algorithms to this setting through case studies for various well-known parameterised problems.
Cite as

Jonas Schmidt, Thomas Schwentick, Nils Vortmeier, Thomas Zeume, and Ioannis Kokkinis. Dynamic Complexity Meets Parameterised Algorithms. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 36:1-36:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{schmidt_et_al:LIPIcs.CSL.2020.36,
  author =	{Schmidt, Jonas and Schwentick, Thomas and Vortmeier, Nils and Zeume, Thomas and Kokkinis, Ioannis},
  title =	{{Dynamic Complexity Meets Parameterised Algorithms}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{36:1--36:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Fern\'{a}ndez, Maribel and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.36},
  URN =		{urn:nbn:de:0030-drops-116792},
  doi =		{10.4230/LIPIcs.CSL.2020.36},
  annote =	{Keywords: Dynamic complexity, parameterised complexity}
}
Document
DOI: 10.4230/LIPIcs.CSL.2020.37
Dynamic Complexity of Parity Exists Queries

Authors: Nils Vortmeier and Thomas Zeume

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)

Abstract
Given a graph whose nodes may be coloured red, the parity of the number of red nodes can easily be maintained with first-order update rules in the dynamic complexity framework DynFO of Patnaik and Immerman. Can this be generalised to other or even all queries that are definable in first-order logic extended by parity quantifiers? We consider the query that asks whether the number of nodes that have an edge to a red node is odd. Already this simple query of quantifier structure parity-exists is a major roadblock for dynamically capturing extensions of first-order logic. We show that this query cannot be maintained with quantifier-free first-order update rules, and that variants induce a hierarchy for such update rules with respect to the arity of the maintained auxiliary relations. Towards maintaining the query with full first-order update rules, it is shown that degree-restricted variants can be maintained.
Cite as

Nils Vortmeier and Thomas Zeume. Dynamic Complexity of Parity Exists Queries. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 37:1-37:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{vortmeier_et_al:LIPIcs.CSL.2020.37,
  author =	{Vortmeier, Nils and Zeume, Thomas},
  title =	{{Dynamic Complexity of Parity Exists Queries}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{37:1--37:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Fern\'{a}ndez, Maribel and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.37},
  URN =		{urn:nbn:de:0030-drops-116805},
  doi =		{10.4230/LIPIcs.CSL.2020.37},
  annote =	{Keywords: Dynamic complexity, parity quantifier, arity hierarchy}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.120
Reachability and Distances under Multiple Changes

Authors: Samir Datta, Anish Mukherjee, Nils Vortmeier, and Thomas Zeume

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

Abstract
Recently it was shown that the transitive closure of a directed graph can be updated using first-order formulas after insertions and deletions of single edges in the dynamic descriptive complexity framework by Dong, Su, and Topor, and Patnaik and Immerman. In other words, Reachability is in DynFO. In this article we extend the framework to changes of multiple edges at a time, and study the Reachability and Distance queries under these changes. We show that the former problem can be maintained in DynFO(+, x) under changes affecting O({log n}/{log log n}) nodes, for graphs with n nodes. If the update formulas may use a majority quantifier then both Reachability and Distance can be maintained under changes that affect O(log^c n) nodes, for fixed c in N. Some preliminary results towards showing that distances are in DynFO are discussed.
Cite as

Samir Datta, Anish Mukherjee, Nils Vortmeier, and Thomas Zeume. Reachability and Distances under Multiple Changes. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 120:1-120:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{datta_et_al:LIPIcs.ICALP.2018.120,
  author =	{Datta, Samir and Mukherjee, Anish and Vortmeier, Nils and Zeume, Thomas},
  title =	{{Reachability and Distances under Multiple Changes}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{120:1--120:14},
  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.2018.120},
  URN =		{urn:nbn:de:0030-drops-91245},
  doi =		{10.4230/LIPIcs.ICALP.2018.120},
  annote =	{Keywords: dynamic complexity, reachability, distances, complex changes}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2018.3
An Update on Dynamic Complexity Theory

Authors: Thomas Zeume

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

Abstract
In many modern data management scenarios, data is subject to frequent changes. In order to avoid costly re-computing query answers from scratch after each small update, one can try to use auxiliary relations that have been computed before. Of course, the auxiliary relations need to be updated dynamically whenever the data changes. Dynamic complexity theory studies which queries and auxiliary relations can be updated in a highly parallel fashion, that is, by constant-depth circuits or, equivalently, by first-order formulas or the relational algebra. After gently introducing dynamic complexity theory, I will discuss recent results of the area with a focus on the dynamic complexity of the reachability query.
Cite as

Thomas Zeume. An Update on Dynamic Complexity Theory. In 21st International Conference on Database Theory (ICDT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 98, p. 3:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{zeume:LIPIcs.ICDT.2018.3,
  author =	{Zeume, Thomas},
  title =	{{An Update on Dynamic Complexity Theory}},
  booktitle =	{21st International Conference on Database Theory (ICDT 2018)},
  pages =	{3:1--3:1},
  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.2018.3},
  URN =		{urn:nbn:de:0030-drops-86117},
  doi =		{10.4230/LIPIcs.ICDT.2018.3},
  annote =	{Keywords: Dynamic descriptive complexity, SQL updates, Reachability}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2018.7
A More General Theory of Static Approximations for Conjunctive Queries

Authors: Pablo Barceló, Miguel Romero, and Thomas Zeume

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

Abstract
Conjunctive query (CQ) evaluation is NP-complete, but becomes tractable for fragments of bounded hypertreewidth. If a CQ is hard to evaluate, it is thus useful to evaluate an approximation of it in such fragments. While underapproximations (i.e., those that return correct answers only) are well-understood, the dual notion of overapproximations that return complete (but not necessarily sound) answers, and also a more general notion of approximation based on the symmetric difference of query results, are almost unexplored. In fact, the decidability of the basic problems of evaluation, identification, and existence of those approximations, is open. We develop a connection with existential pebble game tools that allows the systematic study of such problems. In particular, we show that the evaluation and identification of overapproximations can be solved in polynomial time. We also make progress in the problem of existence of overapproximations, showing it to be decidable in 2EXPTIME over the class of acyclic CQs. Furthermore, we look at when overapproximations do not exist, suggesting that this can be alleviated by using a more liberal notion of overapproximation. We also show how to extend our tools to study symmetric difference approximations. We observe that such approximations properly extend under- and over-approximations, settle the complexity of its associated identification problem, and provide several results on existence and evaluation.
Cite as

Pablo Barceló, Miguel Romero, and Thomas Zeume. A More General Theory of Static Approximations for Conjunctive Queries. In 21st International Conference on Database Theory (ICDT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 98, pp. 7:1-7:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{barcelo_et_al:LIPIcs.ICDT.2018.7,
  author =	{Barcel\'{o}, Pablo and Romero, Miguel and Zeume, Thomas},
  title =	{{A More General Theory of Static Approximations for Conjunctive Queries}},
  booktitle =	{21st International Conference on Database Theory (ICDT 2018)},
  pages =	{7:1--7:22},
  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.2018.7},
  URN =		{urn:nbn:de:0030-drops-86021},
  doi =		{10.4230/LIPIcs.ICDT.2018.7},
  annote =	{Keywords: conjunctive queries, hypertreewidth, approximations, pebble games}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.98
A Strategy for Dynamic Programs: Start over and Muddle Through

Authors: Samir Datta, Anish Mukherjee, Thomas Schwentick, Nils Vortmeier, and Thomas Zeume

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
A strategy for constructing dynamic programs is introduced that utilises periodic computation of auxiliary data from scratch and the ability to maintain a query for a limited number of change steps. It is established that if some program can maintain a query for log n change steps after an AC^1-computable initialisation, it can be maintained by a first-order dynamic program as well, i.e., in DynFO. As an application, it is shown that decision and optimisation problems defined by monadic second-order (MSO) and guarded second-order logic (GSO) formulas are in DynFO, if only change sequences that produce graphs of bounded treewidth are allowed. To establish this result, Feferman-Vaught-type composition theorems for MSO and GSO are established that might be useful in their own right.
Cite as

Samir Datta, Anish Mukherjee, Thomas Schwentick, Nils Vortmeier, and Thomas Zeume. A Strategy for Dynamic Programs: Start over and Muddle Through. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 98:1-98:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{datta_et_al:LIPIcs.ICALP.2017.98,
  author =	{Datta, Samir and Mukherjee, Anish and Schwentick, Thomas and Vortmeier, Nils and Zeume, Thomas},
  title =	{{A Strategy for Dynamic Programs: Start over and Muddle Through}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{98:1--98:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.98},
  URN =		{urn:nbn:de:0030-drops-74470},
  doi =		{10.4230/LIPIcs.ICALP.2017.98},
  annote =	{Keywords: dynamic complexity, treewidth, monadic second order logic}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2017.19
Dynamic Complexity under Definable Changes

Authors: Thomas Schwentick, Nils Vortmeier, and Thomas Zeume

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

Abstract
This paper studies dynamic complexity under definable change operations in the DynFO framework by Patnaik and Immerman. It is shown that for changes definable by parameter-free first-order formulas, all (uniform) AC1 queries can be maintained by first-order dynamic programs. Furthermore, many maintenance results for single-tuple changes are extended to more powerful change operations: (1) The reachability query for undirected graphs is first-order maintainable under single tuple changes and first-order defined insertions, likewise the reachability query for directed acyclic graphs under quantifier-free insertions. (2) Context-free languages are first-order maintainable under \EFO-defined changes. These results are complemented by several inexpressibility results, for example, that the reachability query cannot be maintained by quantifier-free programs under definable, quantifier-free deletions.
Cite as

Thomas Schwentick, Nils Vortmeier, and Thomas Zeume. Dynamic Complexity under Definable Changes. In 20th International Conference on Database Theory (ICDT 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 68, pp. 19:1-19:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{schwentick_et_al:LIPIcs.ICDT.2017.19,
  author =	{Schwentick, Thomas and Vortmeier, Nils and Zeume, Thomas},
  title =	{{Dynamic Complexity under Definable Changes}},
  booktitle =	{20th International Conference on Database Theory (ICDT 2017)},
  pages =	{19:1--19:18},
  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.2017.19},
  URN =		{urn:nbn:de:0030-drops-70596},
  doi =		{10.4230/LIPIcs.ICDT.2017.19},
  annote =	{Keywords: dynamic descriptive complexity, SQL updates, dynamic programs}
}
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