A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

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

2018
*
arXiv
*
pre-print

We study the first-order (

arXiv:1805.01823v1
fatcat:i6b567eaavf4rdncmg2nahwqwe
*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*. ...##
###
A New Perspective on FO Model Checking of Dense Graph Classes

2016
*
Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16
*

We study the

doi:10.1145/2933575.2935314
dblp:conf/lics/GajarskyHOLR16
fatcat:ygcxdwpwvvbwnpgd4rz62acemy
*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. ...##
###
First-order limits, an analytical perspective

2016
*
European journal of combinatorics (Print)
*

In this paper we present

doi:10.1016/j.ejc.2015.07.012
fatcat:bd5u5kga6fd3xioa6cpbqrpkny
*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*). ...##
###
On the Parameterized Complexity of Learning First-Order Logic
[article]

2021
*
arXiv
*
pre-print

The first is

arXiv:2102.12201v2
fatcat:qe6rwrwzjbdshfxnq4s5f57gja
*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*. ...##
###
FO Model Checking on Posets of Bounded Width
[article]

2015
*
arXiv
*
pre-print

for

arXiv:1504.04115v2
fatcat:2bmwaakfync6fkwg2agtkckivy
*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. ...##
###
Stable graphs of bounded twin-width

2022
*
Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science
*

It also implies that monadically stable

doi:10.1145/3531130.3533356
fatcat:odelyxerdbd5vb7onkwtkar5wm
*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 ...##
###
FO Model Checking on Posets of Bounded Width

2015
*
2015 IEEE 56th Annual Symposium on Foundations of Computer Science
*

The parameterized complexity

doi:10.1109/focs.2015.63
dblp:conf/focs/GajarskyHLOORS15
fatcat:2h4ymkxotfbnfpplhh6v4aqza4
*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*. ...##
###
Faster Deciding MSO Properties of Trees of Fixed Height, and Some Consequences

2012
*
Foundations of Software Technology and Theoretical Computer Science
*

This yields

doi:10.4230/lipics.fsttcs.2012.112
dblp:conf/fsttcs/GajarskyH12
fatcat:wit3in442fe4pn23tikkr6d54y
*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". ...##
###
A Generalization of the Łoś-Tarski Preservation Theorem - Dissertation Summary
[article]

2018
*
arXiv
*
pre-print

The constructive aspects

arXiv:1811.01014v1
fatcat:vurmh3kcrbgtve7yp6lqngflpy
*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*...##
###
A unified approach to structural limits, and limits of graphs with bounded tree-depth
[article]

2013
*
arXiv
*
pre-print

In this paper we introduce

arXiv:1303.6471v2
fatcat:4k4qq7ku2rdvpcekx6bhf567xq
*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*. ...##
###
First Order Logic and Twin-Width in Tournaments and Dense Oriented Graphs
[article]

2022
*
arXiv
*
pre-print

We characterise the

arXiv:2207.07683v2
fatcat:zsn7ltcj65boxm2qp4vaoaozs4
*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. ...##
###
When Trees Grow Low: Shrubs and Fast MSO1
[chapter]

2012
*
Lecture Notes in Computer Science
*

To prove that MSO1

doi:10.1007/978-3-642-32589-2_38
fatcat:ngfzh2gylrdhlbqeqr5fzaci4i
*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 ...##
###
Local certification of MSO properties for bounded treedepth graphs
[article]

2021
*
arXiv
*
pre-print

The

arXiv:2110.01936v1
fatcat:344p5alkczaxfgn7xnmm63ah2q
*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] . ...##
###
Algorithms and data structures for first-order logic with connectivity under vertex failures
[article]

2021
*
arXiv
*
pre-print

We prove that the

arXiv:2111.03725v1
fatcat:wedmyezosvdhhchducwqxrbz4a
*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 ...##
###
Twin-width VI: the lens of contraction sequences
[article]

2022
*
arXiv
*
pre-print

MSO_1)

arXiv:2111.00282v2
fatcat:2jrgz5lmffclvmlwwnsbzq5spy
*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 ...
« Previous

*Showing results 1 — 15 out of 1,928 results*