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A New Perspective on FO Model Checking of Dense Graph Classes [article]

Jakub Gajarský, Petr Hliněný, Daniel Lokshtanov, Jan Obdržálek, M.S. Ramanujan
2018 arXiv   pre-print
We study the first-order (FO) model checking problem of dense graphs, namely those which have FO interpretations in (or are FO transductions of) some sparse graph classes.  ...  As a consequence, we obtain an FPT algorithm for successor-invariant FO model checking of any graph class which is FO interpretable in (or an FO transduction of) a graph class of bounded degree.  ...  dense, then the FO model checking problem on D is as hard as that on all graphs.  ... 
arXiv:1805.01823v1 fatcat:i6b567eaavf4rdncmg2nahwqwe

A New Perspective on FO Model Checking of Dense Graph Classes

J. Gajarský, P. Hliněný, J. Obdržálek, D. Lokshtanov, M. S. Ramanujan
2016 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16  
We study the FO model checking problem of dense graph classes, namely those which are FO-interpretable in some sparse graph classes.  ...  As a consequence, we obtain an FPT algorithm for FO model checking of graph classes FO interpretable in graph classes of bounded degree.  ...  Acknowledgments We would like to thank the anonymous referees for careful reading of the paper and for the many helpful suggestions and remarks. J. Gajarský, P. Hliněný and J.  ... 
doi:10.1145/2933575.2935314 dblp:conf/lics/GajarskyHOLR16 fatcat:ygcxdwpwvvbwnpgd4rz62acemy

First-order limits, an analytical perspective

Jaroslav Nešetřil, Patrice Ossona de Mendez
2016 European journal of combinatorics (Print)  
In this paper we present a novel approach to graph (and structural) limits based on model theory and analysis.  ...  As an application, it leads to new intermediate examples of structural convergence and to a "grand conjecture" dealing with sparse graphs. We survey the recent developments.  ...  This also leads to a new characterization of nowhere dense classes. Convex Combinations. Definition 20 (Convex combination of Modelings).  ... 
doi:10.1016/j.ejc.2015.07.012 fatcat:bd5u5kga6fd3xioa6cpbqrpkny

On the Parameterized Complexity of Learning First-Order Logic [article]

Steffen van Bergerem, Martin Grohe, Martin Ritzert
2021 arXiv   pre-print
The first is a hardness result, showing that learning first-order queries is at least as hard as the corresponding model-checking problem, which implies that on general structures it is hard for the parameterized  ...  We analyse the complexity of learning first-order queries in a model-theoretic framework for supervised learning introduced by (Grohe and Tur\'an, TOCS 2004).  ...  One of the most general family of graph classes with a tractable first-order model-checking problem is the family of effectively nowhere dense graph classes.  ... 
arXiv:2102.12201v2 fatcat:qe6rwrwzjbdshfxnq4s5f57gja

FO Model Checking on Posets of Bounded Width [article]

Jakub Gajarský, Petr Hliněný, Daniel Lokshtanov, Jan Obdržálek, Sebastian Ordyniak, M. S. Ramanujan, Saket Saurabh
2015 arXiv   pre-print
for FO model checking of nowhere dense classes of graphs [STOC'14], with dense structures starting to attract attention only recently.  ...  Bova, Ganian and Szeider showed that model checking existential FO logic is fixed-parameter tractable (FPT) on posets of bounded width, where the width of a poset is the size of the largest antichain in  ...  The parameterized complexity of FO model checking on sparse graph classes is now well understood. In 1994 Seese [21] showed an FPT algorithm for FO model checking on graphs of bounded degree.  ... 
arXiv:1504.04115v2 fatcat:2bmwaakfync6fkwg2agtkckivy

Stable graphs of bounded twin-width

Jakub Gajarský, Michał Pilipczuk, Szymon Toruńczyk
2022 Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science  
It also implies that monadically stable classes of bounded twin-width are linearly χ -bounded. CCS CONCEPTS • Theory of computation → Finite Model Theory; • Mathematics of computing → Graph theory.  ...  We prove that every class of graphs C that is monadically stable and has bounded twin-width can be transduced from some class with bounded sparse twin-width.  ...  ACKNOWLEDGMENTS This paper is a part of projects LIPA (JG) and BOBR (MP, SzT) that have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation  ... 
doi:10.1145/3531130.3533356 fatcat:odelyxerdbd5vb7onkwtkar5wm

FO Model Checking on Posets of Bounded Width

Jakub Gajarsky, Petr Hlineny, Daniel Lokshtanov, Jan Obdralek, Sebastian Ordyniak, M.S. Ramanujan, Saket Saurabh
2015 2015 IEEE 56th Annual Symposium on Foundations of Computer Science  
The parameterized complexity of FO model checking on sparse graph classes is now well understood. In 1994 Seese [21] showed an FPT algorithm for FO model checking on graphs of bounded degree.  ...  Most of the research on algorithms for FO model checking has focused on graphs.  ... 
doi:10.1109/focs.2015.63 dblp:conf/focs/GajarskyHLOORS15 fatcat:2h4ymkxotfbnfpplhh6v4aqza4

Faster Deciding MSO Properties of Trees of Fixed Height, and Some Consequences

Jakub Gajarsky, Petr Hlineny, Marc Herbstritt
2012 Foundations of Software Technology and Theoretical Computer Science  
This yields a faster MSO model checking algorithm for trees of bounded height than the one for general trees.  ...  This makes bounded shrub-depth a good candidate for characterization of the hereditary classes of graphs on which FO and MSO 1 coincide, a problem recently posed by Elberfeld, Grohe, and Tantau (LICS 2012  ...  Thomas [7] showing linear-time FPT decidability of FO model checking on the graphs of "bounded expansion".  ... 
doi:10.4230/lipics.fsttcs.2012.112 dblp:conf/fsttcs/GajarskyH12 fatcat:wit3in442fe4pn23tikkr6d54y

A Generalization of the Łoś-Tarski Preservation Theorem - Dissertation Summary [article]

Abhisekh Sankaran
2018 arXiv   pre-print
The constructive aspects of the proofs of the model-theoretic results of the dissertation are used to obtain (algorithmic) meta-kernels for various dense graphs such as graphs of bounded clique-width and  ...  subclasses of these like m-partite cographs and graph classes of bounded shrub-depth.  ...  Structural graph theory of sparse graph classes: On the dual front, k-ary covers play a central role in graphs of bounded expansion and nowhere dense graphs [23] , as seen from the characterizations of  ... 
arXiv:1811.01014v1 fatcat:vurmh3kcrbgtve7yp6lqngflpy

A unified approach to structural limits, and limits of graphs with bounded tree-depth [article]

Jaroslav Nesetril
2013 arXiv   pre-print
In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional) analysis  ...  This limit object is a graph built on a standard probability space with the property that every first-order definable set of tuples is measurable.  ...  graphs cannot be a modeling.  ... 
arXiv:1303.6471v2 fatcat:4k4qq7ku2rdvpcekx6bhf567xq

First Order Logic and Twin-Width in Tournaments and Dense Oriented Graphs [article]

Colin Geniet, Stéphan Thomassé
2022 arXiv   pre-print
We characterise the classes of tournaments with tractable first-order model checking.  ...  For every hereditary class of tournaments 𝒯, first-order model checking either is fixed parameter tractable, or is AW[*]-hard.  ...  First-Order Model Checking on the class of all graphs is AW[ * ]-complete. On classes of structures with bounded twin-width, FO model checking is FPT as long as a witness of twin-width is given.  ... 
arXiv:2207.07683v2 fatcat:zsn7ltcj65boxm2qp4vaoaozs4

When Trees Grow Low: Shrubs and Fast MSO1 [chapter]

Robert Ganian, Petr Hliněný, Jaroslav Nešetřil, Jan Obdržálek, Patrice Ossona de Mendez, Reshma Ramadurai
2012 Lecture Notes in Computer Science  
To prove that MSO1 model checking is fast for classes of bounded shrub-depth, we show that shrub-depth exactly characterizes the graph classes having interpretation in coloured trees of bounded height.  ...  Looking for a similar characterization for (coloured) MSO1, we introduce the notion of shrub-depth of a graph class.  ...  A useful tool when solving the model checking problem on a class of structures is the ability to "efficiently translate" an instance of the problem to a different class of structures, for which we already  ... 
doi:10.1007/978-3-642-32589-2_38 fatcat:ngfzh2gylrdhlbqeqr5fzaci4i

Local certification of MSO properties for bounded treedepth graphs [article]

Nicolas Bousquet, Laurent Feuilloley, Théo Pierron
2021 arXiv   pre-print
The graph model checking problem consists in testing whether an input graph satisfies a given logical formula.  ...  In that direction, our main result states that any MSO formula can be locally certified on graphs with bounded treedepth with a logarithmic number of bits per node, which is the golden standard in certification  ...  For example, when considering rst order logic (i.e. forbidding quanti cations on sets), the model checking becomes FPT on nowhere dense classes [25] .  ... 
arXiv:2110.01936v1 fatcat:344p5alkczaxfgn7xnmm63ah2q

Algorithms and data structures for first-order logic with connectivity under vertex failures [article]

Michał Pilipczuk, Nicole Schirrmacher, Sebastian Siebertz, Szymon Toruńczyk, Alexandre Vigny
2021 arXiv   pre-print
We prove that the model-checking problem for separator logic is fixed-parameter tractable on every class of graphs that exclude a fixed topological minor. We also show a weak converse.  ...  The backbone of our proof relies on a decomposition theorem of Cygan et al. [SICOMP '19], which provides a tree decomposition of a given graph into bags that are unbreakable.  ...  Acknowledgements. e authors thank Mikołaj Boja ńczyk for helpful discussions on separator logic, as well as Anna Zych-Pawlewicz for pointers to the literature on connectivity oracles under vertex failures  ... 
arXiv:2111.03725v1 fatcat:wedmyezosvdhhchducwqxrbz4a

Twin-width VI: the lens of contraction sequences [article]

Édouard Bonnet, Eun Jung Kim, Amadeus Reinald, Stéphan Thomassé
2022 arXiv   pre-print
MSO_1) model checking on graphs with bounded tree-width (resp. bounded rank-width) is fixed-parameter tractable in the size of the input sentence.  ...  A contraction sequence of a graph consists of iteratively merging two of its vertices until only one vertex remains.  ...  On the one hand, it can be seen as a first attempt to unify and extend tractable FO model-checking algorithms on "sparse" classes (bounded degree, bounded expansion) and on possibly "dense" classes (bounded  ... 
arXiv:2111.00282v2 fatcat:2jrgz5lmffclvmlwwnsbzq5spy
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