DROPS

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DOI: 10.4230/LIPIcs.ICDT.2026.16

Gamma Acyclicity, Annotated Relations, and Consistency Witness Functions

Authors: Albert Atserias and Phokion G. Kolaitis

Published in: LIPIcs, Volume 365, 29th International Conference on Database Theory (ICDT 2026)

Abstract

During the early days of relational database theory it was realized that "acyclic" database schemas possess a number of desirable properties. In fact, three different notions of "acyclicity" were identified and investigated during the 1980s, namely, α-acyclicity, β-acyclicity, and γ-acyclicity. Much more recently, the study of α-acyclicity was extended to annotated relations, where the annotations are values from some positive commutative monoid. The recent results about α-acyclic schemas and annotated relations give rise to results about β-acyclic schemas and annotated relations, since a schema is β-acyclic if and only if every sub-schema of it is α-acyclic. Here, we study γ-acyclic schemas and annotated relations. Our main finding is that the characterization of γ-acyclic schemas in terms of monotone sequential join expression extends to annotated relations, provided the annotations come from a positive commutative monoid that has the inner consistency property. Furthermore, the results reported here shed light on the role of the join of two standard relations. Specifically, our results reveal that the only relevant property of the join of two standard relations is that it is a witness to the consistency of the two relations, provided that these two relations are consistent. For the more abstract setting of annotated relations, this property of the standard join is captured by the notion of a consistency witness function, a notion which we systematically utilize in this work.

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Albert Atserias and Phokion G. Kolaitis. Gamma Acyclicity, Annotated Relations, and Consistency Witness Functions. In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{atserias_et_al:LIPIcs.ICDT.2026.16,
  author =	{Atserias, Albert and Kolaitis, Phokion G.},
  title =	{{Gamma Acyclicity, Annotated Relations, and Consistency Witness Functions}},
  booktitle =	{29th International Conference on Database Theory (ICDT 2026)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-413-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{365},
  editor =	{ten Cate, Balder and Funk, Maurice},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2026.16},
  URN =		{urn:nbn:de:0030-drops-256304},
  doi =		{10.4230/LIPIcs.ICDT.2026.16},
  annote =	{Keywords: annotated relations, gamma-acyclicity, consistency witness functions}
}

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Invited Talk

DOI: 10.4230/LIPIcs.STACS.2026.1

Query Languages for Machine-Learning Models (Invited Talk)

Authors: Martin Grohe

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract

In my invited talk and this accompanying paper, I discuss two logics for weighted finite structures: first-order logic with summation (FO(SUM)) and its recursive extension IFP(SUM). These logics originate from foundational work by Grädel, Gurevich, and Meer in the 1990s. In recent joint work with Standke, Steegmans, and Van den Bussche, we have investigated these logics as query languages for machine learning models, specifically neural networks, which are naturally represented as weighted graphs. I present illustrative examples of queries to neural networks that can be expressed in these logics and discuss fundamental results on their expressiveness and computational complexity.

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Martin Grohe. Query Languages for Machine-Learning Models (Invited Talk). In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{grohe:LIPIcs.STACS.2026.1,
  author =	{Grohe, Martin},
  title =	{{Query Languages for Machine-Learning Models}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.1},
  URN =		{urn:nbn:de:0030-drops-254904},
  doi =		{10.4230/LIPIcs.STACS.2026.1},
  annote =	{Keywords: Expressive power of query languages, fixed-point logics, weighted structures, neural networks, explainable AI}
}

Document

Research

DOI: 10.4230/TGDK.3.3.1

A Logic Programming Approach to Repairing SHACL Constraint Violations

Authors: Shqiponja Ahmetaj, Robert David, Axel Polleres, and Mantas Šimkus

Published in: TGDK, Volume 3, Issue 3 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 3

Abstract

The Shapes Constraint Language (SHACL) is a recent standard, a W3C recommendation, for validating RDF graphs against shape constraints to be checked on target nodes of a data graph. The standard also describes the notion of validation reports, which detail the results of the validation process. In case of violation of constraints, the validation report should explain the reasons for non-validation, offering guidance on how to identify or fix violations in the data graph. Since the specification left it open to SHACL processors to define such explanations, a recent work proposed the use of explanations in the style of database repairs, where a repair is a set of additions to or deletions from the data graph so that the resulting graph validates against the constraints. In this paper, we study such repairs for non-recursive SHACL, the largest fragment of SHACL that is fully defined in the specification. We propose an algorithm to compute repairs by encoding the explanation problem - using Answer Set Programming (ASP) - into a logic program, where the answer sets contain (minimal) repairs. We then study a scenario where it is not possible to simultaneously repair all the targets, which may be the case due to overall unsatisfiability or conflicting constraints. We introduce a relaxed notion of validation, which allows to validate a (maximal) subset of the targets and adapt the ASP translation to take into account this relaxation. Finally, we add support for repairing constraints which use property paths and equality of paths. Our implementation in clingo is - to the best of our knowledge - the first implementation of a repair program for SHACL.

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Shqiponja Ahmetaj, Robert David, Axel Polleres, and Mantas Šimkus. A Logic Programming Approach to Repairing SHACL Constraint Violations. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 3, pp. 1:1-1:36, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{ahmetaj_et_al:TGDK.3.3.1,
  author =	{Ahmetaj, Shqiponja and David, Robert and Polleres, Axel and \v{S}imkus, Mantas},
  title =	{{A Logic Programming Approach to Repairing SHACL Constraint Violations}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{1:1--1:36},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{3},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.3.1},
  URN =		{urn:nbn:de:0030-drops-252124},
  doi =		{10.4230/TGDK.3.3.1},
  annote =	{Keywords: SHACL, Shapes Constraint Language, Database Repairs, Knowledge Graphs, Semantic Web, Answer Set Programming}
}

Document

Invited Paper

DOI: 10.4230/OASIcs.RW.2024/2025.2

Fine-Grained Complexity of Ontology Mediated Queries (Invited Paper)

Authors: Cristina Feier

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract

This article surveys some approaches for establishing fine-grained complexity results for evaluation of ontology mediated queries (OMQs). It accompanies a related talk given at the Reasoning Web Summer School 2024. It zooms into some characterizations of efficiency in a parameterized complexity framework for OMQs based on various description logics and guarded tgds. As such results were established using results from query evaluation on databases, it also discusses the relevant results from the database world. After surveying some successive results on OMQs which all leverage database results in custom ways, it describes an approach which provides a general fpt reduction from query evaluation in the database world to query evaluation in the OMQ world. The reduction enables porting hardness results from the DB world to the OMQ world in a black-box fashion. Along these mentioned approaches, it also provides a brief survey of other approaches which are concerned with fine-grained complexity of OMQs and are based on rewriting techniques.

Cite as

Cristina Feier. Fine-Grained Complexity of Ontology Mediated Queries (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{feier:OASIcs.RW.2024/2025.2,
  author =	{Feier, Cristina},
  title =	{{Fine-Grained Complexity of Ontology Mediated Queries}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{2:1--2:23},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.2},
  URN =		{urn:nbn:de:0030-drops-250476},
  doi =		{10.4230/OASIcs.RW.2024/2025.2},
  annote =	{Keywords: complexity analysis, guarded logics, guarded tgds, database theory, ontology mediated queries}
}

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Invited Paper

DOI: 10.4230/OASIcs.RW.2024/2025.3

Foundations of Graph Neural Networks (A Logician’s View) (Invited Paper)

Authors: Egor V. Kostylev

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract

Graph Neural Networks (GNNs) are a family of neural architectures that are naturally suited to learning functions on graphs. They are now used in a wide range of applications. It has been observed that GNNs share many similarities with classical computer science (CS) formalisms, such as the Weisfeiler-Leman graph isomorphism test, bisimulation, and logic. Most notably, both GNNs and these formalisms deal with functions on graphs and graph-like structures. This observation opens up an opportunity to compare GNN architectures with these formalisms in terms of different kinds of expressibility, thus positioning these architectures within the well-established landscape of theoretical CS. This, in turn, helps us better understand the fundamental capabilities and limitations of various GNN architectures, enabling more informed choices about which architecture to use - if any at all. In these lecture notes, I give an introduction to the state-of-the-art foundations of GNNs - specifically, our current understanding of their expressibility in terms of the classical formalisms, considering several notions of expressive power.

Cite as

Egor V. Kostylev. Foundations of Graph Neural Networks (A Logician’s View) (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kostylev:OASIcs.RW.2024/2025.3,
  author =	{Kostylev, Egor V.},
  title =	{{Foundations of Graph Neural Networks (A Logician’s View)}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{3:1--3:19},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.3},
  URN =		{urn:nbn:de:0030-drops-250486},
  doi =		{10.4230/OASIcs.RW.2024/2025.3},
  annote =	{Keywords: Graph Neural Networks, Expressivity, Logic}
}

Document

DOI: 10.4230/LIPIcs.TQC.2025.5

Towards a Complexity-Theoretic Dichotomy for TQFT Invariants

Authors: Nicolas Bridges and Eric Samperton

Published in: LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)

Abstract

We show that for any fixed (2+1)-dimensional TQFT over ℂ of either Turaev-Viro-Barrett-Westbury or Reshetikhin-Turaev type, the problem of (exactly) computing its invariants on closed 3-manifolds is either solvable in polynomial time, or else it is #𝖯-hard to (exactly) contract certain tensors that are built from the TQFT’s fusion category. Our proof is an application of a dichotomy result of Cai and Chen [J. ACM, 2017] concerning weighted constraint satisfaction problems over ℂ. We leave for future work the issue of reinterpreting the conditions of Cai and Chen that distinguish between the two cases (i.e. #𝖯-hard tensor contractions vs. polynomial time invariants) in terms of fusion categories. We expect that with more effort, our reduction can be improved so that one gets a dichotomy directly for TQFTs' invariants of 3-manifolds rather than more general tensors built from TQFTs' fusion categories.

Cite as

Nicolas Bridges and Eric Samperton. Towards a Complexity-Theoretic Dichotomy for TQFT Invariants. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bridges_et_al:LIPIcs.TQC.2025.5,
  author =	{Bridges, Nicolas and Samperton, Eric},
  title =	{{Towards a Complexity-Theoretic Dichotomy for TQFT Invariants}},
  booktitle =	{20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
  pages =	{5:1--5:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-392-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{350},
  editor =	{Fefferman, Bill},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.5},
  URN =		{urn:nbn:de:0030-drops-240548},
  doi =		{10.4230/LIPIcs.TQC.2025.5},
  annote =	{Keywords: Complexity, topological quantum field theory, dichotomy theorems, constraint satisfaction problems, tensor categories}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2025.61

Quantum Relaxations of CSP and Structure Isomorphism

Authors: Amin Karamlou

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract

We investigate quantum relaxations of two key decision problems in computer science: the constraint satisfaction problem (CSP) and the structure isomorphism problem. CSP asks whether a homomorphism exists between two relational structures, while structure isomorphism seeks an isomorphism between them. In recent years, it has become increasingly apparent that many special cases of CSP can be reformulated in terms of the existence of perfect classical strategies in non-local games, a key topic of study in quantum information theory. These games have allowed us to study quantum advantage in relation to many important decision problems, such as the k-colouring problem, and the problem of solving binary constraint systems. Abramsky et al. (2017) have shown that all of these games can be seen as special instances of a non-local CSP game. Moreover, they show that perfect quantum strategies in this CSP game can be viewed as Kleisli morphisms of a graded monad on the category of relational structures, which they dub the quantum monad. In this way, the quantum monad provides a categorical characterisation of quantum advantage for the non-local CSP game. In this work we solidify and expand the results of Abramsky et al., answering several of their open questions. Firstly, we compare the definition of quantum graph homomorphisms arising from this work with an earlier definition of the concept due to Mančinska and Roberson and show that there are graphs which exhibit quantum advantage under one definition but not the other. Our second contribution is to extend the results of Abramsky et al. which only hold in the tensor product framework of quantum mechanics to the commuting operator framework. Next, we study a non-local structure isomorphism game, which generalises the well-studied graph isomorphism game. We show how the construction of the quantum monad can be refined to provide categorical semantics for quantum strategies in this game. This results in a category where morphisms coincide with quantum homomorphisms and isomorphisms coincide with quantum isomorphisms.

Cite as

Amin Karamlou. Quantum Relaxations of CSP and Structure Isomorphism. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 61:1-61:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{karamlou:LIPIcs.MFCS.2025.61,
  author =	{Karamlou, Amin},
  title =	{{Quantum Relaxations of CSP and Structure Isomorphism}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{61:1--61:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.61},
  URN =		{urn:nbn:de:0030-drops-241686},
  doi =		{10.4230/LIPIcs.MFCS.2025.61},
  annote =	{Keywords: CSP, graph isomorphism, quantum information, non-local game, quantum graph homomorphism, monad}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2025.9

Linear Time Subsequence and Supersequence Regex Matching

Authors: Antoine Amarilli, Florin Manea, Tina Ringleb, and Markus L. Schmid

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract

It is well-known that checking whether a given string w matches a given regular expression r can be done in quadratic time O(|w|⋅ |r|) and that this cannot be improved to a truly subquadratic running time of O((|w|⋅ |r|)^{1-ε}) assuming the strong exponential time hypothesis (SETH). We study a different matching paradigm where we ask instead whether w has a subsequence that matches r, and show that regex matching in this sense can be solved in linear time O(|w| + |r|). Further, the same holds if we ask for a supersequence. We show that the quantitative variants where we want to compute a longest or shortest subsequence or supersequence of w that matches r can be solved in O(|w|⋅ |r|), i. e., asymptotically no worse than classical regex matching; and we show that O(|w| + |r|) is conditionally not possible for these problems. We also investigate these questions with respect to other natural string relations like the infix, prefix, left-extension or extension relation instead of the subsequence and supersequence relation. We further study the complexity of the universal problem where we ask if all subsequences (or supersequences, infixes, prefixes, left-extensions or extensions) of an input string satisfy a given regular expression.

Cite as

Antoine Amarilli, Florin Manea, Tina Ringleb, and Markus L. Schmid. Linear Time Subsequence and Supersequence Regex Matching. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{amarilli_et_al:LIPIcs.MFCS.2025.9,
  author =	{Amarilli, Antoine and Manea, Florin and Ringleb, Tina and Schmid, Markus L.},
  title =	{{Linear Time Subsequence and Supersequence Regex Matching}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.9},
  URN =		{urn:nbn:de:0030-drops-241162},
  doi =		{10.4230/LIPIcs.MFCS.2025.9},
  annote =	{Keywords: subsequence, supersequence, regular language, regular expression, automata}
}

Document

DOI: 10.4230/OASIcs.Manzini.14

BWT Indexes for Optimal Joins in Graph Databases

Authors: Diego Arroyuelo and Gonzalo Navarro

Published in: OASIcs, Volume 131, The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday (2025)

Abstract

Graph databases represent data as a labeled directed graph, where the labels refer to properties that connect the entities represented by their source and target vertices. Queries feature, most prominently, sets of edges where source, target, and/or label can be variables; each instantiation of the variables where all the edges occur in the graph is a solution to the query. Worst-case-optimal algorithms to solve those queries have been devised, but they pose significant space requirements. This overhead has hindered the adoption of worst-case-optimal algorithms in real systems. We show that a representation of the graph based on the extended BWT (eBWT), where each edge is seen as an independent string of length 3 (source, label, target) supports worst-case-optimal algorithms while using almost no extra space on top of the raw data. We then show how the idea is generalized to the relational model, where the strings can be longer than 3 and several eBWTs are needed to obtain worst-case optimality. The aim to minimize the amount of space in that case leads to consider novel eBWT variants, where columns other than the last can be chosen. Finally, we show how the same graph representation can be used to solve other typical queries, like finding graph paths that match regular expressions.

Cite as

Diego Arroyuelo and Gonzalo Navarro. BWT Indexes for Optimal Joins in Graph Databases. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{arroyuelo_et_al:OASIcs.Manzini.14,
  author =	{Arroyuelo, Diego and Navarro, Gonzalo},
  title =	{{BWT Indexes for Optimal Joins in Graph Databases}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{14:1--14:19},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.14},
  URN =		{urn:nbn:de:0030-drops-239222},
  doi =		{10.4230/OASIcs.Manzini.14},
  annote =	{Keywords: Graph databases, Ring index, extended BWT, compact data structures}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2025.30

Coherent Tietze Transformations of 1-Polygraphs in Homotopy Type Theory

Authors: Samuel Mimram and Émile Oleon

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract

Polygraphs play a fundamental role in algebra, geometry, and computer science, by generalizing group presentations to higher-dimensional structures and encoding coherence for those. They have recently been adapted by Kraus and von Raumer to the setting of homotopy type theory, where they are useful to define and study higher inductive types. Here, we develop the theory of 1-dimensional polygraphs, which correspond to presentations of sets in homotopy type theory. This requires us to introduce a dedicated notion of Tietze transformation, generalizing their well-known counterpart in group theory: the equivalence generated by those transformations characterizes situations where two 1-polygraphs present the same set. We also show a homotopy transfer theorem, which provides a way to transport coherence structures from one 1-polygraph to another. This work lays the foundations for a general theory of polygraphs in arbitrary dimensions, which should be useful for instance to define and study coherent group presentations, allowing for synthetic (co)homology computations. Most of the results in the article have been formalized with the Agda proof assistant using the cubical HoTT library.

Cite as

Samuel Mimram and Émile Oleon. Coherent Tietze Transformations of 1-Polygraphs in Homotopy Type Theory. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 30:1-30:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mimram_et_al:LIPIcs.FSCD.2025.30,
  author =	{Mimram, Samuel and Oleon, \'{E}mile},
  title =	{{Coherent Tietze Transformations of 1-Polygraphs in Homotopy Type Theory}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{30:1--30:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.30},
  URN =		{urn:nbn:de:0030-drops-236456},
  doi =		{10.4230/LIPIcs.FSCD.2025.30},
  annote =	{Keywords: homotopy type theory, polygraph, Tietze transformation, coherence}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2025.30

In-Memory Object Graph Stores

Authors: Aditya Thimmaiah, Zijian Yi, Joseph Kenis, Christopher J Rossbach, and Milos Gligoric

Published in: LIPIcs, Volume 333, 39th European Conference on Object-Oriented Programming (ECOOP 2025)

Abstract

We present a design and implementation of an in-memory object graph store, dubbed εStore. Our key innovation is a storage model - epsilon store - that equates an object on the heap to a node in a graph store. Thus any object on the heap (without changes) can be a part of one, or multiple, graph stores, and vice versa, any node in a graph store can be accessed like any other object on the heap. Specifically, each node in a graph is an object (i.e., instance of a class), and its properties and its edges are the primitive and reference fields declared in its class, respectively. Necessary classes, which are instantiated to represent nodes, are created dynamically by εStore. εStore uses a subset of the Cypher query language to query the graph store. By design, the result of any query is a table (ResultSet) of references to objects on the heap, which users can manipulate the same way as any other object on the heap in their programs. Moreover, a developer can include (transitively) an arbitrary object to become a part of a graph store. Finally, εStore introduces compile-time rewriting of Cypher queries into imperative code to improve the runtime performance. εStore can be used for a number of tasks including implementing methods for complex in-memory structures, writing complex assertions, or a stripped down version of a graph database that can conveniently be used during testing. We implement εStore in Java and show its application using the aforementioned tasks.

Cite as

Aditya Thimmaiah, Zijian Yi, Joseph Kenis, Christopher J Rossbach, and Milos Gligoric. In-Memory Object Graph Stores. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 30:1-30:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{thimmaiah_et_al:LIPIcs.ECOOP.2025.30,
  author =	{Thimmaiah, Aditya and Yi, Zijian and Kenis, Joseph and Rossbach, Christopher J and Gligoric, Milos},
  title =	{{In-Memory Object Graph Stores}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{30:1--30:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-373-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{333},
  editor =	{Aldrich, Jonathan and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2025.30},
  URN =		{urn:nbn:de:0030-drops-233225},
  doi =		{10.4230/LIPIcs.ECOOP.2025.30},
  annote =	{Keywords: Object stores, Graph stores, Cypher}
}

Document

DOI: 10.4230/LIPIcs.ICDT.2025.31

On Deciding the Data Complexity of Answering Linear Monadic Datalog Queries with LTL Operators

Authors: Alessandro Artale, Anton Gnatenko, Vladislav Ryzhikov, and Michael Zakharyaschev

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract

Our concern is the data complexity of answering linear monadic datalog queries whose atoms in the rule bodies can be prefixed by operators of linear temporal logic LTL. We first observe that, for data complexity, answering any connected query with operators ○/○- (at the next/previous moment) is either in AC⁰, or in ACC⁰\AC⁰, or NC¹-complete, or L-hard and in NL. Then we show that the problem of deciding L-hardness of answering such queries is PSpace-complete, while checking membership in the classes AC⁰ and ACC⁰ as well as NC¹-completeness can be done in ExpSpace. Finally, we prove that membership in AC⁰ or in ACC⁰, NC¹-completeness, and L-hardness are undecidable for queries with operators ◇/◇- (sometime in the future/past) provided that NC¹ ≠ NL and L ≠ NL.

Cite as

Alessandro Artale, Anton Gnatenko, Vladislav Ryzhikov, and Michael Zakharyaschev. On Deciding the Data Complexity of Answering Linear Monadic Datalog Queries with LTL Operators. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{artale_et_al:LIPIcs.ICDT.2025.31,
  author =	{Artale, Alessandro and Gnatenko, Anton and Ryzhikov, Vladislav and Zakharyaschev, Michael},
  title =	{{On Deciding the Data Complexity of Answering Linear Monadic Datalog Queries with LTL Operators}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.31},
  URN =		{urn:nbn:de:0030-drops-229723},
  doi =		{10.4230/LIPIcs.ICDT.2025.31},
  annote =	{Keywords: Linear monadic datalog, linear temporal logic, data complexity}
}

Document

DOI: 10.4230/LIPIcs.CSL.2025.14

Finite Variable Counting Logics with Restricted Requantification

Authors: Simon Raßmann, Georg Schindling, and Pascal Schweitzer

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract

Counting logics with a bounded number of variables form one of the central concepts in descriptive complexity theory. Although they restrict the number of variables that a formula can contain, the variables can be nested within scopes of quantified occurrences of themselves. In other words, the variables can be requantified. We study the fragments obtained from counting logics by restricting requantification for some but not necessarily all the variables. Similar to the logics without limitation on requantification, we develop tools to investigate the restricted variants. Specifically, we introduce a bijective pebble game in which certain pebbles can only be placed once and for all, and a corresponding two-parametric family of Weisfeiler-Leman algorithms. We show close correspondences between the three concepts. By using a suitable cops-and-robber game and adaptations of the Cai-Fürer-Immerman construction, we completely clarify the relative expressive power of the new logics. We show that the restriction of requantification has beneficial algorithmic implications in terms of graph identification. Indeed, we argue that with regard to space complexity, non-requantifiable variables only incur an additive polynomial factor when testing for equivalence. In contrast, for all we know, requantifiable variables incur a multiplicative linear factor. Finally, we observe that graphs of bounded tree-depth and 3-connected planar graphs can be identified using no, respectively, only a very limited number of requantifiable variables.

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Simon Raßmann, Georg Schindling, and Pascal Schweitzer. Finite Variable Counting Logics with Restricted Requantification. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 14:1-14:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ramann_et_al:LIPIcs.CSL.2025.14,
  author =	{Ra{\ss}mann, Simon and Schindling, Georg and Schweitzer, Pascal},
  title =	{{Finite Variable Counting Logics with Restricted Requantification}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{14:1--14:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.14},
  URN =		{urn:nbn:de:0030-drops-227716},
  doi =		{10.4230/LIPIcs.CSL.2025.14},
  annote =	{Keywords: Requantification, Finite variable counting logics, Weisfeiler-Leman algorithm}
}

Document

Survey

DOI: 10.4230/TGDK.2.1.3

Semantic Web: Past, Present, and Future

Authors: Ansgar Scherp, Gerd Groener, Petr Škoda, Katja Hose, and Maria-Esther Vidal

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract

Ever since the vision was formulated, the Semantic Web has inspired many generations of innovations. Semantic technologies have been used to share vast amounts of information on the Web, enhance them with semantics to give them meaning, and enable inference and reasoning on them. Throughout the years, semantic technologies, and in particular knowledge graphs, have been used in search engines, data integration, enterprise settings, and machine learning. In this paper, we recap the classical concepts and foundations of the Semantic Web as well as modern and recent concepts and applications, building upon these foundations. The classical topics we cover include knowledge representation, creating and validating knowledge on the Web, reasoning and linking, and distributed querying. We enhance this classical view of the so-called "Semantic Web Layer Cake" with an update of recent concepts that include provenance, security and trust, as well as a discussion of practical impacts from industry-led contributions. We conclude with an outlook on the future directions of the Semantic Web. This is a living document. If you like to contribute, please contact the first author and visit: https://github.com/ascherp/semantic-web-primer

Cite as

Ansgar Scherp, Gerd Groener, Petr Škoda, Katja Hose, and Maria-Esther Vidal. Semantic Web: Past, Present, and Future. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 3:1-3:37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{scherp_et_al:TGDK.2.1.3,
  author =	{Scherp, Ansgar and Groener, Gerd and \v{S}koda, Petr and Hose, Katja and Vidal, Maria-Esther},
  title =	{{Semantic Web: Past, Present, and Future}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{3:1--3:37},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.3},
  URN =		{urn:nbn:de:0030-drops-198607},
  doi =		{10.4230/TGDK.2.1.3},
  annote =	{Keywords: Linked Open Data, Semantic Web Graphs, Knowledge Graphs}
}

Document

DOI: 10.4230/LIPIcs.CALCO.2017.19

A Classical Groupoid Model for Quantum Networks

Authors: David Reutter and Jamie Vicary

Published in: LIPIcs, Volume 72, 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)

Abstract

We give a mathematical analysis of a new type of classical computer network architecture, intended as a model of a new technology that has recently been proposed in industry. Our approach is based on groubits, generalizations of classical bits based on groupoids. This network architecture allows the direct execution of a number of protocols that are usually associated with quantum networks, including teleportation, dense coding and secure key distribution.

Cite as

David Reutter and Jamie Vicary. A Classical Groupoid Model for Quantum Networks. In 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 72, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{reutter_et_al:LIPIcs.CALCO.2017.19,
  author =	{Reutter, David and Vicary, Jamie},
  title =	{{A Classical Groupoid Model for Quantum Networks}},
  booktitle =	{7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)},
  pages =	{19:1--19:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-033-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{72},
  editor =	{Bonchi, Filippo and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2017.19},
  URN =		{urn:nbn:de:0030-drops-80391},
  doi =		{10.4230/LIPIcs.CALCO.2017.19},
  annote =	{Keywords: groupoids, networks, quantum, semantics, key distribution}
}

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