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**Published in:** LIPIcs, Volume 290, 27th International Conference on Database Theory (ICDT 2024)

When extracting a relation of spans (intervals) from a text document, a common practice is to filter out tuples of the relation that are deemed dominated by others. The domination rule is defined as a partial order that varies along different systems and tasks. For example, we may state that a tuple is dominated by tuples that extend it by assigning additional attributes, or assigning larger intervals. The result of filtering the relation would then be the skyline according to this partial order. As this filtering may remove most of the extracted tuples, we study whether we can improve the performance of the extraction by compiling the domination rule into the extractor.
To this aim, we introduce the skyline operator for declarative information extraction tasks expressed as document spanners. We show that this operator can be expressed via regular operations when the domination partial order can itself be expressed as a regular spanner, which covers several natural domination rules. Yet, we show that the skyline operator incurs a computational cost (under combined complexity). First, there are cases where the operator requires an exponential blowup on the number of states needed to represent the spanner as a sequential variable-set automaton. Second, the evaluation may become computationally hard. Our analysis more precisely identifies classes of domination rules for which the combined complexity is tractable or intractable.

Antoine Amarilli, Benny Kimelfeld, Sébastien Labbé, and Stefan Mengel. Skyline Operators for Document Spanners. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{amarilli_et_al:LIPIcs.ICDT.2024.7, author = {Amarilli, Antoine and Kimelfeld, Benny and Labb\'{e}, S\'{e}bastien and Mengel, Stefan}, title = {{Skyline Operators for Document Spanners}}, booktitle = {27th International Conference on Database Theory (ICDT 2024)}, pages = {7:1--7:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-312-6}, ISSN = {1868-8969}, year = {2024}, volume = {290}, editor = {Cormode, Graham and Shekelyan, Michael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2024.7}, URN = {urn:nbn:de:0030-drops-197898}, doi = {10.4230/LIPIcs.ICDT.2024.7}, annote = {Keywords: Information Extraction, Document Spanners, Query Evaluation} }

Document

**Published in:** LIPIcs, Volume 290, 27th International Conference on Database Theory (ICDT 2024)

A central computational task in database theory, finite model theory, and computer science at large is the evaluation of a first-order sentence on a finite structure. In the context of this task, the width of a sentence, defined as the maximum number of free variables over all subformulas, has been established as a crucial measure, where minimizing width of a sentence (while retaining logical equivalence) is considered highly desirable. An undecidability result rules out the possibility of an algorithm that, given a first-order sentence, returns a logically equivalent sentence of minimum width; this result motivates the study of width minimization via syntactic rewriting rules, which is this article’s focus. For a number of common rewriting rules (which are known to preserve logical equivalence), including rules that allow for the movement of quantifiers, we present an algorithm that, given a positive first-order sentence ϕ, outputs the minimum-width sentence obtainable from ϕ via application of these rules. We thus obtain a complete algorithmic understanding of width minimization up to the studied rules; this result is the first one - of which we are aware - that establishes this type of understanding in such a general setting. Our result builds on the theory of term rewriting and establishes an interface among this theory, query evaluation, and structural decomposition theory.

Hubie Chen and Stefan Mengel. Optimally Rewriting Formulas and Database Queries: A Confluence of Term Rewriting, Structural Decomposition, and Complexity. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chen_et_al:LIPIcs.ICDT.2024.16, author = {Chen, Hubie and Mengel, Stefan}, title = {{Optimally Rewriting Formulas and Database Queries: A Confluence of Term Rewriting, Structural Decomposition, and Complexity}}, booktitle = {27th International Conference on Database Theory (ICDT 2024)}, pages = {16:1--16:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-312-6}, ISSN = {1868-8969}, year = {2024}, volume = {290}, editor = {Cormode, Graham and Shekelyan, Michael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2024.16}, URN = {urn:nbn:de:0030-drops-197984}, doi = {10.4230/LIPIcs.ICDT.2024.16}, annote = {Keywords: width, query rewriting, structural decomposition, term rewriting} }

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**Published in:** LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

A central task in knowledge compilation is to compile a CNF-SAT instance into a succinct representation format that allows efficient operations such as testing satisfiability, counting, or enumerating all solutions. Useful representation formats studied in this area range from ordered binary decision diagrams (OBDDs) to circuits in decomposable negation normal form (DNNFs).
While it is known that there exist CNF formulas that require exponential size representations, the situation is less well studied for other types of constraints than Boolean disjunctive clauses. The constraint satisfaction problem (CSP) is a powerful framework that generalizes CNF-SAT by allowing arbitrary sets of constraints over any finite domain. The main goal of our work is to understand for which type of constraints (also called the constraint language) it is possible to efficiently compute representations of polynomial size. We answer this question completely and prove two tight characterizations of efficiently compilable constraint languages, depending on whether target format is structured.
We first identify the combinatorial property of "strong blockwise decomposability" and show that if a constraint language has this property, we can compute DNNF representations of linear size. For all other constraint languages we construct families of CSP-instances that provably require DNNFs of exponential size. For a subclass of "strong uniformly blockwise decomposable" constraint languages we obtain a similar dichotomy for structured DNNFs. In fact, strong (uniform) blockwise decomposability even allows efficient compilation into multi-valued analogs of OBDDs and FBDDs, respectively. Thus, we get complete characterizations for all knowledge compilation classes between O(B)DDs and DNNFs.

Christoph Berkholz, Stefan Mengel, and Hermann Wilhelm. A Characterization of Efficiently Compilable Constraint Languages. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{berkholz_et_al:LIPIcs.STACS.2024.11, author = {Berkholz, Christoph and Mengel, Stefan and Wilhelm, Hermann}, title = {{A Characterization of Efficiently Compilable Constraint Languages}}, booktitle = {41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)}, pages = {11:1--11:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-311-9}, ISSN = {1868-8969}, year = {2024}, volume = {289}, editor = {Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.11}, URN = {urn:nbn:de:0030-drops-197214}, doi = {10.4230/LIPIcs.STACS.2024.11}, annote = {Keywords: constraint satisfaction, knowledge compilation, dichotomy, DNNF} }

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**Published in:** LIPIcs, Volume 271, 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)

We study BDD-based bucket elimination, an approach to satisfiability testing using variable elimination which has seen several practical implementations in the past. We prove that it allows solving the standard pigeonhole principle formulas efficiently, when allowing different orders for variable elimination and BDD-representations, a variant of bucket elimination that was recently introduced. Furthermore, we show that this upper bound is somewhat brittle as for formulas which we get from the pigeonhole principle by restriction, i.e., fixing some of the variables, the same approach with the same variable orders has exponential runtime. We also show that the more common implementation of bucket elimination using the same order for variable elimination and the BDDs has exponential runtime for the pigeonhole principle when using either of the two orders from our upper bound, which suggests that the combination of both is the key to efficiency in the setting.

Stefan Mengel. Bounds on BDD-Based Bucket Elimination. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 16:1-16:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{mengel:LIPIcs.SAT.2023.16, author = {Mengel, Stefan}, title = {{Bounds on BDD-Based Bucket Elimination}}, booktitle = {26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)}, pages = {16:1--16:11}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-286-0}, ISSN = {1868-8969}, year = {2023}, volume = {271}, editor = {Mahajan, Meena and Slivovsky, Friedrich}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2023.16}, URN = {urn:nbn:de:0030-drops-184789}, doi = {10.4230/LIPIcs.SAT.2023.16}, annote = {Keywords: Bucket Elimination, Binary Decision Diagrams, Satisfiability, Complexity} }

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**Published in:** LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)

Rectangle decision lists are a form of decision lists that were recently shown to have applications in the proof complexity of certain OBDD-based QBF-solvers. We consider a version of rectangle decision lists with changing partitions, which corresponds to QBF-solvers that may change the variable order of the OBDDs they produce. We show that even allowing one single partition change generally leads to exponentially more succinct decision lists. More generally, we show that there is a succinctness hierarchy: for every k ∈ ℕ, when going from k partition changes to k+1, there are functions that can be represented exponentially more succinctly. As an application, we show a similar hierarchy for OBDD-based QBF-solvers.

Stefan Mengel. Changing Partitions in Rectangle Decision Lists. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{mengel:LIPIcs.SAT.2022.17, author = {Mengel, Stefan}, title = {{Changing Partitions in Rectangle Decision Lists}}, booktitle = {25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)}, pages = {17:1--17:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-242-6}, ISSN = {1868-8969}, year = {2022}, volume = {236}, editor = {Meel, Kuldeep S. and Strichman, Ofer}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.17}, URN = {urn:nbn:de:0030-drops-166913}, doi = {10.4230/LIPIcs.SAT.2022.17}, annote = {Keywords: rectangle decision lists, QBF proof complexity, OBDD} }

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**Published in:** LIPIcs, Volume 127, 22nd International Conference on Database Theory (ICDT 2019)

We study the complexity of evaluating well-designed pattern trees, a query language extending conjunctive queries with the possibility to define parts of the query to be optional. This possibility of optional parts is important for obtaining meaningful results over incomplete data sources as it is common in semantic web settings.
Recently, a structural characterization of the classes of well-designed pattern trees that can be evaluated in polynomial time was shown. However, projection - a central feature of many query languages - was not considered in this study. We work towards closing this gap by giving a characterization of all tractable classes of simple well-designed pattern trees with projection (under some common complexity theoretic assumptions). Since well-designed pattern trees correspond to the fragment of well-designed {AND, OPTIONAL}-SPARQL queries this gives a complete description of the tractable classes of queries with projections in this fragment that can be characterized by the underlying graph structures of the queries.

Stefan Mengel and Sebastian Skritek. Characterizing Tractability of Simple Well-Designed Pattern Trees with Projection. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{mengel_et_al:LIPIcs.ICDT.2019.20, author = {Mengel, Stefan and Skritek, Sebastian}, title = {{Characterizing Tractability of Simple Well-Designed Pattern Trees with Projection}}, booktitle = {22nd International Conference on Database Theory (ICDT 2019)}, pages = {20:1--20:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-101-6}, ISSN = {1868-8969}, year = {2019}, volume = {127}, editor = {Barcelo, Pablo and Calautti, Marco}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2019.20}, URN = {urn:nbn:de:0030-drops-103220}, doi = {10.4230/LIPIcs.ICDT.2019.20}, annote = {Keywords: SPARQL, well-designed pattern trees, query evaluation, FPT, characterizing tractable classes} }

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**Published in:** LIPIcs, Volume 127, 22nd International Conference on Database Theory (ICDT 2019)

We consider the information extraction framework known as document spanners, and study the problem of efficiently computing the results of the extraction from an input document, where the extraction task is described as a sequential variable-set automaton (VA). We pose this problem in the setting of enumeration algorithms, where we can first run a preprocessing phase and must then produce the results with a small delay between any two consecutive results. Our goal is to have an algorithm which is tractable in combined complexity, i.e., in the sizes of the input document and the VA; while ensuring the best possible data complexity bounds in the input document size, i.e., constant delay in the document size. Several recent works at PODS'18 proposed such algorithms but with linear delay in the document size or with an exponential dependency in size of the (generally nondeterministic) input VA. In particular, Florenzano et al. suggest that our desired runtime guarantees cannot be met for general sequential VAs. We refute this and show that, given a nondeterministic sequential VA and an input document, we can enumerate the mappings of the VA on the document with the following bounds: the preprocessing is linear in the document size and polynomial in the size of the VA, and the delay is independent of the document and polynomial in the size of the VA. The resulting algorithm thus achieves tractability in combined complexity and the best possible data complexity bounds. Moreover, it is rather easy to describe, in particular for the restricted case of so-called extended VAs.

Antoine Amarilli, Pierre Bourhis, Stefan Mengel, and Matthias Niewerth. Constant-Delay Enumeration for Nondeterministic Document Spanners. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{amarilli_et_al:LIPIcs.ICDT.2019.22, author = {Amarilli, Antoine and Bourhis, Pierre and Mengel, Stefan and Niewerth, Matthias}, title = {{Constant-Delay Enumeration for Nondeterministic Document Spanners}}, booktitle = {22nd International Conference on Database Theory (ICDT 2019)}, pages = {22:1--22:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-101-6}, ISSN = {1868-8969}, year = {2019}, volume = {127}, editor = {Barcelo, Pablo and Calautti, Marco}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2019.22}, URN = {urn:nbn:de:0030-drops-103246}, doi = {10.4230/LIPIcs.ICDT.2019.22}, annote = {Keywords: enumeration, spanners, automata} }

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**Published in:** LIPIcs, Volume 126, 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)

We generalize several tractability results concerning the tractability of Quantified Boolean Formulas (QBF) with restricted underlying structure. To this end, we introduce a notion of width for structured DNNF which are a class of Boolean circuits heavily studied in knowledge compilation, a subarea of artificial intelligence. We then show that structured DNNF allow quantifier elimination with a size blow-up depending only on the width of the DNNF and not its size. Using known algorithms transforming restricted CNF-formulas into deterministic DNNF, we apply this result to generalize several results for counting and decision on QBF. We also complement these results with lower bounds that show that our definitions and results are essentially optimal in several senses.

Florent Capelli and Stefan Mengel. Tractable QBF by Knowledge Compilation. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{capelli_et_al:LIPIcs.STACS.2019.18, author = {Capelli, Florent and Mengel, Stefan}, title = {{Tractable QBF by Knowledge Compilation}}, booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)}, pages = {18:1--18:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-100-9}, ISSN = {1868-8969}, year = {2019}, volume = {126}, editor = {Niedermeier, Rolf and Paul, Christophe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.18}, URN = {urn:nbn:de:0030-drops-102571}, doi = {10.4230/LIPIcs.STACS.2019.18}, annote = {Keywords: QBF, knowledge compilation, parameterized algorithms} }

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

We study how to evaluate MSO queries with free variables on trees, within the
framework of enumeration algorithms. Previous work has shown how to enumerate
answers with linear-time preprocessing and delay linear in the size of each
output, i.e., constant-delay for free first-order variables. We extend this
result to support relabelings, a restricted kind of update operations on
trees which allows us to change the node labels. Our main result shows that we
can enumerate the answers of MSO queries on trees with linear-time preprocessing
and delay linear in each answer, while supporting node relabelings in logarithmic time. To
prove this, we reuse the circuit-based enumeration structure from our earlier
work, and develop techniques to maintain its index under node relabelings. We
also show how enumeration under relabelings can be applied to evaluate practical
query languages, such as aggregate, group-by, and parameterized queries.

Antoine Amarilli, Pierre Bourhis, and Stefan Mengel. Enumeration on Trees under Relabelings. In 21st International Conference on Database Theory (ICDT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 98, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{amarilli_et_al:LIPIcs.ICDT.2018.5, author = {Amarilli, Antoine and Bourhis, Pierre and Mengel, Stefan}, title = {{Enumeration on Trees under Relabelings}}, booktitle = {21st International Conference on Database Theory (ICDT 2018)}, pages = {5:1--5:18}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2018.5}, URN = {urn:nbn:de:0030-drops-86060}, doi = {10.4230/LIPIcs.ICDT.2018.5}, annote = {Keywords: enumeration, trees, updates, MSO, circuits, knowledge compilation} }

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

We study the problem of enumerating the satisfying valuations of a circuit while bounding the delay, i.e., the time needed to compute each successive valuation. We focus on the class of structured d-DNNF circuits originally introduced in knowledge compilation, a sub-area of artificial intelligence. We propose an algorithm for these circuits that enumerates valuations with linear preprocessing and delay linear in the Hamming weight of each valuation. Moreover, valuations of constant Hamming weight can be enumerated with linear preprocessing and constant delay.
Our results yield a framework for efficient enumeration that applies to all problems whose solutions can be compiled to structured d-DNNFs. In particular, we use it to recapture classical results in database theory, for factorized database representations and for MSO evaluation. This gives an independent proof of constant-delay enumeration for MSO formulae with first-order free variables on bounded-treewidth structures.

Antoine Amarilli, Pierre Bourhis, Louis Jachiet, and Stefan Mengel. A Circuit-Based Approach to Efficient Enumeration. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 111:1-111:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{amarilli_et_al:LIPIcs.ICALP.2017.111, author = {Amarilli, Antoine and Bourhis, Pierre and Jachiet, Louis and Mengel, Stefan}, title = {{A Circuit-Based Approach to Efficient Enumeration}}, booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, pages = {111:1--111:15}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.111}, URN = {urn:nbn:de:0030-drops-74626}, doi = {10.4230/LIPIcs.ICALP.2017.111}, annote = {Keywords: circuits, constant-delay, enumeration, d-DNNFs, MSO} }

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

Conjunctive queries are basic and heavily studied database queries; in relational algebra, they are the select-project-join queries. In this article, we study the fundamental problem of counting, given a conjunctive query and a relational database, the number of answers to the query on the database. In particular, we study the complexity of this problem relative to sets of conjunctive queries. We present a trichotomy theorem, which shows essentially that this problem on a set of conjunctive queries is either tractable, equivalent to the parameterized CLIQUE problem, or as hard as the parameterized counting CLIQUE problem; the criteria describing which of these situations occurs is simply stated, in terms of graph-theoretic conditions.

Hubie Chen and Stefan Mengel. A Trichotomy in the Complexity of Counting Answers to Conjunctive Queries. In 18th International Conference on Database Theory (ICDT 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 31, pp. 110-126, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{chen_et_al:LIPIcs.ICDT.2015.110, author = {Chen, Hubie and Mengel, Stefan}, title = {{A Trichotomy in the Complexity of Counting Answers to Conjunctive Queries}}, booktitle = {18th International Conference on Database Theory (ICDT 2015)}, pages = {110--126}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2015.110}, URN = {urn:nbn:de:0030-drops-49804}, doi = {10.4230/LIPIcs.ICDT.2015.110}, annote = {Keywords: database theory, query answering, conjunctive queries, counting complexity} }

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**Published in:** LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)

We show that SAT on beta-acyclic CNF-formulas can be solved in polynomial time. In contrast to previous algorithms for other structurally restricted classes of formulas, our algorithm does not proceed by dynamic programming. Instead, it works along an elimination order, solving a weighted version of constraint satisfaction. We give evidence that this deviation from more standard algorithms is no coincidence by showing that it is outside of the framework recently proposed by Saether et al. (SAT 2014) which subsumes all other structural tractability results for #SAT known so far.

Johann Brault-Baron, Florent Capelli, and Stefan Mengel. Understanding Model Counting for beta-acyclic CNF-formulas. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 143-156, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{braultbaron_et_al:LIPIcs.STACS.2015.143, author = {Brault-Baron, Johann and Capelli, Florent and Mengel, Stefan}, title = {{Understanding Model Counting for beta-acyclic CNF-formulas}}, booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)}, pages = {143--156}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-78-1}, ISSN = {1868-8969}, year = {2015}, volume = {30}, editor = {Mayr, Ernst W. and Ollinger, Nicolas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.143}, URN = {urn:nbn:de:0030-drops-49106}, doi = {10.4230/LIPIcs.STACS.2015.143}, annote = {Keywords: model counting, hypergraph acyclicity, structural tractability} }

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**Published in:** LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)

We investigate the algebraic complexity of tensor calulus. We consider a generalization of iterated matrix product to tensors and show that the resulting formulas exactly capture VP, the class of polynomial families efficiently computable by arithmetic circuits. This gives a natural and robust characterization of this complexity class that despite its naturalness is not very well understood so far.

Florent Capelli, Arnaud Durand, and Stefan Mengel. The arithmetic complexity of tensor contractions. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 365-376, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{capelli_et_al:LIPIcs.STACS.2013.365, author = {Capelli, Florent and Durand, Arnaud and Mengel, Stefan}, title = {{The arithmetic complexity of tensor contractions}}, booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)}, pages = {365--376}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-50-7}, ISSN = {1868-8969}, year = {2013}, volume = {20}, editor = {Portier, Natacha and Wilke, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.365}, URN = {urn:nbn:de:0030-drops-39481}, doi = {10.4230/LIPIcs.STACS.2013.365}, annote = {Keywords: algebraic complexity, arithmetic circuits, tensor calculus} }

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

We consider the complexity of two questions on polynomials given by arithmetic circuits: testing whether a monomial is present and counting the number of monomials. We show that these problems are complete for subclasses of the counting hierarchy which had few or no known natural complete problems before. We also study these questions for circuits computing multilinear polynomials.

Hervé Fournier, Guillaume Malod, and Stefan Mengel. Monomials in arithmetic circuits: Complete problems in the counting hierarchy. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 362-373, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{fournier_et_al:LIPIcs.STACS.2012.362, author = {Fournier, Herv\'{e} and Malod, Guillaume and Mengel, Stefan}, title = {{Monomials in arithmetic circuits: Complete problems in the counting hierarchy}}, booktitle = {29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)}, pages = {362--373}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.362}, URN = {urn:nbn:de:0030-drops-34240}, doi = {10.4230/LIPIcs.STACS.2012.362}, annote = {Keywords: arithmetic circuits, counting problems, polynomials} }

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