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Definability and Descriptive Complexity on Databases of Bounded Tree-Width [chapter]

Martin Grohe, Julian Mariño
1999 Lecture Notes in Computer Science  
We study the expressive power of various query languages on relational databases of bounded tree-width.  ...  We then prove a general definability theorem stating that each query on a class of databases of bounded tree-width which is definable in monadic second-order logic is also definable in fixed-point logic  ...  definable on graphs of bounded tree-width.  ... 
doi:10.1007/3-540-49257-7_6 fatcat:4yje2r6bmbfbjmjpa7d7nt3xge

Circuits, Logic and Games (Dagstuhl Seminar 15401)

Mikolaj Bojanczyk, Meena Mahajan, Thomas Schwentick, Heribert Vollmer, Marc Herbstritt
2016 Dagstuhl Reports  
complexity and circuit lower bounds inherently using methods from logic and algebra Proof systems with low circuit complexity Dynamic complexity: understanding the dynamic expressive power of small depth  ...  Over the years, there has been a lot of interplay between circuit complexity and logic.  ...  In the light of isomorphism for trees being hard for the complexity class logspace, this makes the ubiquitous class of graphs of bounded tree width one of the few classes of graphs for which the complexity  ... 
doi:10.4230/dagrep.5.9.105 dblp:journals/dagstuhl-reports/BojanczykMSV15 fatcat:pv6oxt7lnvhkbczugwxmvumdxq

Towards Efficient Reasoning Under Guarded-Based Disjunctive Existential Rules [chapter]

Pierre Bourhis, Michael Morak, Andreas Pieris
2014 Lecture Notes in Computer Science  
We show that (unions of) conjunctive queries of bounded hypertreewidth and of bounded treewidth do not reduce the complexity of our problem, even if we focus on predicates of bounded arity, or on fixed  ...  Three of the most prominent subclasses of this kind are queries of bounded hypertree-width, queries of bounded treewidth and acyclic queries.  ...  Pierre thankfully acknowledges projetéquipe associée Inria North-European Labs 2013-2016, Michael his DOC Fellowship of the Austrian Academy of Sciences, and Andreas the EPSRC grant EP/J008346/1 (PrO-QAW  ... 
doi:10.1007/978-3-662-44522-8_9 fatcat:ed5vyvl625eahipnvcy3c3jnt4

When is Ontology-Mediated Querying Efficient? [article]

Pablo Barcelo, Cristina Feier, Carsten Lutz, Andreas Pieris
2020 arXiv   pre-print
Both results are in terms of equivalence to OMQs of bounded tree width and rest on a reasonable assumption from parameterized complexity theory.  ...  We further study the complexity of the meta problem of deciding whether a given OMQ is equivalent to an OMQ of bounded tree width, providing several completeness results that range from NP to 2ExpTime,  ...  This research was supported by ERC consolidator grant 647289 CODA, by EPSRC grant EP/S003800/1 EQUID, by the Millennium Institute for Foundational Research on Data, and Fondecyt grant 1170109.  ... 
arXiv:2003.07800v2 fatcat:egn75xzrlbarrkt74rajqwwbo4

Hypertree Decompositions: A Survey [chapter]

Georg Gottlob, Nicola Leone, Francesco Scarcello
2001 Lecture Notes in Computer Science  
This paper surveys recent results related to the concept of hypertree decomposition and the associated notion of hypertree width.  ...  We also review a number of complexity results on problems whose structure is described by acyclic or nearly acyclic hypergraphs.  ...  Research supported by FWF (Austrian Science Funds) under the project Z29-INF (Wittgenstein Award), and by MURST under project COFIN-2000 "From Data to Information (D2I)"  ... 
doi:10.1007/3-540-44683-4_5 fatcat:e2x57x7rdbesflhlesjfs6426e

First-Order Rewritability of Frontier-Guarded Ontology-Mediated Queries

Pablo Barceló, Gerald Berger, Carsten Lutz, Andreas Pieris
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
The first approach employs standard two-way alternating parity tree automata. Although it does not lead to a tight complexity bound, it provides a transparent solution based on widely known tools.  ...  We focus on ontology-mediated queries (OMQs) based on (frontier-)guarded existential rules and (unions of) conjunctive queries, and we investigate the problem of FO-rewritability, i.e., whether an OMQ  ...  Upper bounds. The fact that for predicates of bounded arity FORew(G, AQ 0 ) is in EXPTIME is obtained from Theorem 9. It remains to show that FORew(FG, UCQ) is in 2EX-PTIME.  ... 
doi:10.24963/ijcai.2018/236 dblp:conf/ijcai/BarceloBLP18 fatcat:pv7kdhiyyrbk3k65j4rog5g3hu

Semantically Acyclic Conjunctive Queries under Functional Dependencies

Diego Figueira
2016 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16  
However, acyclic CQs and CQs of bounded tree-width can be evaluated in polynomial time in combined complexity and they are fixed-parameter tractable.  ...  We study the problem of whether a CQ can be rewritten into an equivalent CQ of bounded tree-width, in the presence of unary functional dependencies, assuming bounded arity signatures.  ...  Acknowledgements I am grateful to Pablo Barceló and Miguel Romero for having introduced me to this subject, and to anonymous reviewers for helpful comments.  ... 
doi:10.1145/2933575.2933580 dblp:conf/lics/Figueira16 fatcat:nm7f7e7osrcnddlizmundfrsce

Classifying the Complexity of Ontology-Mediated Queries in EL: From Atomic Queries to Conjunctive Queries (Extended Abstract)

Carsten Lutz, Leif Sabellek
2020 International Workshop on Description Logics  
Traditionally, data complexity and rewritability have mostly been studied on the level of OMQ languages (L, Q) defined by an ontology language L such as EL and a query language Q such as conjunctive queries  ...  We report on [14], which carries out a fine-grained analysis of the data complexity and rewritability of OMQs from (EL, CQ), achieving a complete classification.  ...  We say that Q has bounded depth if there is a constant bound on the depth of the trees in M Q and Q has bounded pathwidth if there is a constant bound on the pathwidth of the trees in M Q ; recall that  ... 
dblp:conf/dlog/LutzS20 fatcat:26ragga3erbs3aszhbifzprnku

When is Ontology-Mediated Querying Efficient?

Pablo Barcelo, Cristina Feier, Carsten Lutz, Andreas Pieris
2019 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
Both results are in terms of equivalence to OMQs of bounded tree width and rest on a reasonable assumption from parameterized complexity theory.  ...  We further study the complexity of the meta problem of deciding whether a given OMQ is equivalent to an OMQ of bounded tree width, providing several completeness results that range from NP to 2EXPTIME,  ...  We next describe the unraveling of a database into a (potentially infinite) database of bounded tree width. Let D be a database and k ≥ 1.  ... 
doi:10.1109/lics.2019.8785823 dblp:conf/lics/BarceloFLP19 fatcat:qoh3ojvefjaa5os4i7hwrdi5uy

Query answering exploiting structural properties

Francesco Scarcello
2005 SIGMOD record  
Indeed, a number of relevant problems from different areas, such as database theory, artificial intelligence, and game theory, are tractable when their underlying hypergraphs have small (i.e., bounded  ...  We review the notion of hypertree width, a measure of the degree of cyclicity of hypergraphs that is useful for identifying and solving efficiently easy instances of hard problems, by exploiting their  ...  Acknowledgments The author sincerely thanks Georg Gottlob and Nicola Leone, who worked with him on these issues since 1999, when they jointly defined the notion of hypertree decompositions.  ... 
doi:10.1145/1084805.1084827 fatcat:enicq2ngqrbinnr2lkohxxzc7y

Enumerating Homomorphisms [article]

Andrei A. Bulatov, Victor Dalmau, Martin Grohe, Daniel Marx
2009 arXiv   pre-print
The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory.  ...  The decision version of the homomorphism problem received a lot of attention in literature; in particular, the way the graph-theoretical structure of the variables and constraints influences the complexity  ...  "difference between A i and A i−1 " has bounded tree width.  ... 
arXiv:0902.1256v1 fatcat:tu25yj6rnzgtnowgkdei3gqrsi

Characterizing Tractability of Simple Well-Designed Pattern Trees with Projection

Stefan Mengel, Sebastian Skritek, Michael Wagner
2019 International Conference on Database Theory  
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.  ...  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  ...  The width of (T, ν) is (max {|ν(s)| | s ∈ V (T )}) − 1. The treewidth of G is the minimum width of its tree decompositions.  ... 
doi:10.4230/lipics.icdt.2019.20 dblp:conf/icdt/MengelS19 fatcat:ojtopuk6dbh23mxiz7v3cy437u

One hierarchy spawns another

Hubie Chen, Moritz Müller
2014 Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14  
This binary relation is defined in terms of a notion which we call graph deconstruction and which is a variant of the well-known notion of tree decomposition.  ...  In particular, we define a binary relation on graph classes and completely describe the resulting hierarchy given by this relation.  ...  Acknowledgments The first author was supported by the Spanish Project FORMAL-ISM (TIN2007-66523), by the Basque Government Project S-PE12UN050(SAI12/219), and by the University of the Basque Country under  ... 
doi:10.1145/2603088.2603107 dblp:conf/csl/ChenM14 fatcat:xi2ezg25e5cnppnpfho4u27h2i

Hypertree Decompositions and Tractable Queries

Georg Gottlob, Nicola Leone, Francesco Scarcello
2002 Journal of computer and system sciences (Print)  
Examples are the evaluation of Boolean CQs and query containment. These problems were shown tractable for conjunctive queries of bounded treewidth and of bounded degree of cyclicity.  ...  The so far most general concept of nearly acyclic queries was the notion of queries of bounded query-width introduced by Chekuri and Rajaraman (1997).  ...  A LOGCFL Algorithm Deciding k-Bounded Hypertree-Width To each computation tree y of k-decomp on input query Q, we associate a hypertree d(y)=OT, q, lP, called the witness tree of y, defined as follows:  ... 
doi:10.1006/jcss.2001.1809 fatcat:eixkkrj5zzbp7gblcvergbzzbu

Unifying tree decompositions for reasoning in graphical models

Kalev Kask, Rina Dechter, Javier Larrosa, Avi Dechter
2005 Artificial Intelligence  
The paper provides a unifying perspective of tree-decomposition algorithms appearing in various automated reasoning areas such as join-tree clustering for constraint-satisfaction and the cliquetree algorithm  ...  Within this framework, we introduce a new algorithm, called bucket-tree elimination (BTE), that extends Bucket Elimination (BE) to trees, and show that it can provide a speed-up of n over BE for various  ...  in the hyper-tree decomposition hw its hyper-width and t is a bound on the size of the relational representation of each function in R.  ... 
doi:10.1016/j.artint.2005.04.004 fatcat:bi5goekuzrccpdzsf3evjv5jv4
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