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Tree-Width for First Order Formulae
[chapter]

2009
*
Lecture Notes in Computer Science
*

We introduce

doi:10.1007/978-3-642-04027-6_8
fatcat:b2ayc5nucvb3ljf2znqii3ghrm
*tree*-*width**for**first**order**formulae*ϕ, fotw(ϕ). We show that computing fotw is fixed-parameter tractable with parameter fotw. ... In this way, Chen and Dalmau obtain a notion of elimination-*width*1 , which 1 Actually, the notion is called*tree*-*width**for*quantified constraint*formulae*in [9] , But since the notion is defined via elimination ...*TREE*-*WIDTH**FOR**FIRST**ORDER**FORMULAE*5 3.*First**order**tree*-*width*3.1. Stratified*tree*-*width*. We start with defining stratified*tree*-*width*. Then,*first**order**tree*-*width*is defined as a special case. ...##
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Tree-width for first order formulae

2012
*
Logical Methods in Computer Science
*

We introduce

doi:10.2168/lmcs-8(1:32)2012
fatcat:faq5y4oa6rddxfdkpjdjnc6eb4
*tree*-*width**for**first**order**formulae*\phi, fotw(\phi). We show that computing fotw is fixed-parameter tractable with parameter fotw. ... Our notion of*tree*-*width*generalises*tree*-*width*of conjunctive queries to arbitrary*formulae*of*first**order*logic by taking into account the quantifier interaction in a*formula*. ...*TREE*-*WIDTH**FOR**FIRST**ORDER**FORMULAE*5 3.*First**order**tree*-*width*3.1. Stratified*tree*-*width*. We start with defining stratified*tree*-*width*. Then,*first**order**tree*-*width*is defined as a special case. ...##
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Query evaluation via tree-decompositions

2002
*
Journal of the ACM
*

We generalize a theorem of Courcelle [2] by showing that on structures of bounded

doi:10.1145/602220.602222
fatcat:t3zwdhdqdjesndualpsi3cixou
*tree*-*width*a monadic second-*order**formula*(with free*first*-and second-*order*variables) can be evaluated in time linear ... We generalize the notions of acyclicity and bounded*tree*-*width*from conjunctive queries to arbitrary*first*-*order**formulas*in a straightforward way and analyze the complexity of evaluating*formulas*of these ... We generalize a theorem of Courcelle [2] by showing that on structures of bounded*tree*-*width*a monadic second-*order**formula*(with free*first*-and second-*order*variables) can be evaluated in time linear ...##
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Query Evaluation via Tree-Decompositions
[chapter]

2001
*
Lecture Notes in Computer Science
*

We generalize a theorem of Courcelle [2] by showing that on structures of bounded

doi:10.1007/3-540-44503-x_2
fatcat:ozgbjfyezrdmfmbblvofhfhb2y
*tree*-*width*a monadic second-*order**formula*(with free*first*-and second-*order*variables) can be evaluated in time linear ... We generalize the notions of acyclicity and bounded*tree*-*width*from conjunctive queries to arbitrary*first*-*order**formulas*in a straightforward way and analyze the complexity of evaluating*formulas*of these ... We generalize a theorem of Courcelle [2] by showing that on structures of bounded*tree*-*width*a monadic second-*order**formula*(with free*first*-and second-*order*variables) can be evaluated in time linear ...##
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On the Complexity of Resolution-based Proof Systems

2013
*
Bulletin of the European Association for Theoretical Computer Science
*

The

dblp:journals/eatcs/Oliva13
fatcat:tegco4ztnvfe7jjjcx63n2pyx4
*first*result of this thesis is that TQBF, the problem of determining if a fully-quantified propositional CNF-*formula*is true, is PSPACE-complete even when restricted to instances of bounded*tree*-*width*... On the negative side, our*first*result implies that, unless NP = PSPACE, the class of fully-quantified CNF-*formulas*of bounded*tree*-*width*does not have short proofs in any proof system (and in particular ... 3.1*Tree*-*width*and path-*width*. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Quantified boolean*formulas*. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...##
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Definability and Descriptive Complexity on Databases of Bounded Tree-Width
[chapter]

1999
*
Lecture Notes in Computer Science
*

Furthermore,

doi:10.1007/3-540-49257-7_6
fatcat:4yje2r6bmbfbjmjpa7d7nt3xge
*for*each ½ the class of databases of*tree*-*width*at most is definable in fixed-point logic. ... Our*first*theorem says that fixed-point logic with counting captures polynomial time on classes of databases of bounded*tree*-*width*. ... The set of IFP-*formulas*is obtained adding the following*formula*-formation rule to the usual rules to form*first*-*order**formulas*: Given a*formula*³ over the schema , where is a -ary relation symbol*for*...##
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Learnability and Definability in Trees and Similar Structures

2004
*
Theory of Computing Systems
*

We show that monadic second-

doi:10.1007/s00224-003-1112-8
fatcat:myaxkm645zg5zorfkla24llnhu
*order*(MSO)*formulas*with parameters have bounded Vapnik-Chervonenkis dimension over structures of bounded clique-*width*, and*first*-*order**formulas*with parameters have bounded ... We also show that MSO*formulas*of a fixed size have bounded strong consistency dimension over MSO*formulas*of a fixed larger size,*for*labeled*trees*. ... We also show that*first*-*order**formulas*with parameters have bounded VCdimension*for*classes of structures of bounded local clique-*width*. ...##
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Graph Structure and Monadic Second-Order Logic: Language Theoretical Aspects
[chapter]

2008
*
Lecture Notes in Computer Science
*

Hierarchical decompositions yielding the notions of

doi:10.1007/978-3-540-70575-8_1
fatcat:ftpcqszcb5fs5nswbqnbnmy5ja
*tree*-*width*and clique-*width*, expressed by terms written with appropriate graph operations and associated with Monadic Second-*order*Logic are important ... tools*for*the construction of Fixed-Parameter Tractable algorithms and also*for*the extension of methods and results of Formal Language Theory to the description of sets of finite graphs. ... Walukiewicz*for*many useful comments on a*first*draft of this overview. The*first*11 references are books and survey articles. ...##
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Learnability and Definability in Trees and Similar Structures
[chapter]

2002
*
Lecture Notes in Computer Science
*

We show that monadic second-

doi:10.1007/3-540-45841-7_53
fatcat:ypcer5wsh5eo7kh7pxkbbvubc4
*order*(MSO)*formulas*with parameters have bounded Vapnik-Chervonenkis dimension over structures of bounded clique-*width*, and*first*-*order**formulas*with parameters have bounded ... We also show that MSO*formulas*of a fixed size have bounded strong consistency dimension over MSO*formulas*of a fixed larger size,*for*labeled*trees*. ... We also show that*first*-*order**formulas*with parameters have bounded VCdimension*for*classes of structures of bounded local clique-*width*. ...##
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Algorithmic Meta-Theorems
[article]

2009
*
arXiv
*
pre-print

As many meta-theorems use results from graph minor theory, we give a brief introduction to the theory developed by Robertson and Seymour

arXiv:0902.3616v1
fatcat:wsuguljgrvfndhxlsps2ibes2i
*for*their proof of the graph minor theorem and state the main algorithmic ... Many thanks to Javier Esparza*for*proofreading this manuscript and*for*his patience as an editor. ... Acknowledgements I want to take this opportunity to express my gratitude towards Martin Grohe*for*the long discussions we had on graph minors and*for*his advise, patience and inspiration during the time ...##
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Monadic Second-Order Logic for Graphs: Algorithmic and Language Theoretical Applications
[chapter]

2009
*
Lecture Notes in Computer Science
*

This tutorial will present an overview of the use of Monadic Second-

doi:10.1007/978-3-642-00982-2_2
fatcat:ryjvoaa7dnefrcruygfnpqso2i
*Order*Logic to describe sets of finite graphs and graph transformations, in relation with the notions of*tree*-*width*and clique-*width*. ...*First*-*order**formulas*are rather weak in this respect because they can only express local properties, like having degree or diameter at most k*for*fixed k. ...*Tree*-*width*and clique-*width*are important*for*language theoretical issues as well as*for*the construction of polynomial algorithms. ...##
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Deciding first-order properties of locally tree-decomposable structures
[article]

2000
*
arXiv
*
pre-print

We show that

arXiv:cs/0004007v1
fatcat:yhr7ooestza45ayjc7be4f567u
*for*each property P of structures that is definable in*first*-*order*logic and*for*each locally*tree*-decomposable class C of graphs, there is a linear time algorithm deciding whether a given ...*For*classes C of bounded local*tree*-*width*, we show that*for*every k> 1 there is an algorithm that solves the same problem in time O(n^1+(1/k)) (where n is the cardinality of the input structure). ... Let C be a class of relational structures of bounded local*tree*-*width*and ϕ a*first*-*order*definable property. ...##
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Automata for Monadic Second-Order Model-Checking
[chapter]

2011
*
Lecture Notes in Computer Science
*

Engelfriet : Graph structure and monadic second-

doi:10.1007/978-3-642-24288-5_3
fatcat:yngx6xn555bhjchbvt27wyfgoe
*order*logic, book to be published by Cambridge University Press (740 p.). B.C. : Tutorial in 3 parts presented in Bangalore in 2010. ... Monadic second-*order*logic =*First*-*order*logic on power-set structures =*First*-*order*logic extended with (quantified) set variables denoting subsets of the domains. ... (But this is possible if the graph is linearly*ordered*or if some linear*order*is definable by an MSO*formula*). ...##
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Lower Bounds for the Complexity of Monadic Second-Order Logic

2010
*
2010 25th Annual IEEE Symposium on Logic in Computer Science
*

Courcelle's famous theorem from 1990 states that any property of graphs definable in monadic second-

doi:10.1109/lics.2010.39
dblp:conf/lics/KreutzerT10
fatcat:f6m5vckbgjfotl44spf5rygt3e
*order*logic (MSO2) can be decided in linear time on any class of graphs of bounded*tree*-*width*, or in ... In particular, we show that if C is any class of graphs which is closed under taking sub-graphs and whose*tree*-*width*is not bounded by a poly-logarithmic function (in fact, log c n*for*some small c suffices ... If ϕ(x) is a*formula*with a free*first*-*order*variable x and G is a structure, we write ϕ(G)*for*the set {v ∈ U (G) : [9]*for*more on MSO 2 . G |= ϕ[v]}. ...##
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Query Preserving Watermarking Schemes for Locally Treelike Databases

2019
*
Foundations of Software Technology and Theoretical Computer Science
*

We prove that

doi:10.4230/lipics.fsttcs.2019.36
dblp:conf/fsttcs/ChattopadhyayP19
fatcat:vyecore2onayvoml34pdaf4xi4
*for*relational structures whose Gaifman graphs belong to a class of graphs that have locally bounded*tree*-*width*and is closed under minors, watermarking schemes exist that preserve*first*-*order*...*For*relational structures whose Gaifman graphs have bounded degree, watermarking can be done preserving*first*-*order*queries. ... Why*first*-*order*logic? ...
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