Graph Structure and Monadic Second-Order Logic: Language Theoretical Aspects

@inproceedings{Courcelle2008GraphSA,
  title={Graph Structure and Monadic Second-Order Logic: Language Theoretical Aspects},
  author={Bruno Courcelle},
  booktitle={ICALP},
  year={2008}
}
Graph structureis a flexible concept covering many different types of graph properties. Hierarchical decompositions yielding the notions of tree-width and clique-width, expressed by terms written with appropriate graph operations and associated with Monadic Second-order Logicare 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. This informal… 
View via Publisher
labri.fr
14 Citations
Highly Influential Citations
1
Background Citations
5

14 Citations

Monadic Second-Order Logic for Graphs: Algorithmic and Language Theoretical Applications
This tutorial will present an overview of the use of Monadic Second-Order Logic to describe sets of finite graphs and graph transformations, in relation with the notions of tree-width and…
Distributed Graph Automata
  • Fabian Reiter
  • Computer Science, Mathematics
    2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
  • 2015
TLDR
A new class of finite graph automata that recognize precisely the languages of finite graphs definable in monadic second-order logic is introduced.
Courcelle's theorem - A game-theoretic approach
An Auxiliary Logic on Trees: on the Tower-Hardness of Logics Featuring Reachability and Submodel Reasoning
TLDR
A set of simple features are described that are sufficient in order to make the satisfiability problem of logics interpreted on trees Tower-hard and it is proved that this logic is captured by four other logics that were independently found to be Tower-complete.
The enumeration of vertex induced subgraphs with respect to the number of components
Graph and Election Problems Parameterized by Feedback Set Numbers
TLDR
This work investigates the parameterized complexity of three related graph modification problems, given a directed graph, a distinguished vertex, and a positive integer k, with respect to the parameters "treewidth", " size of a feedback vertex set" and "size of a Feedback arc set".
Quantifiers and n-ary binders: an OpenMath standard enhancement proposal
It is proposed that the restriction in the OpenMath standard that an OMBIND element must have exactly three children should be lifted, to support more general binder symbols. The case of logics with…
The Stackelberg minimum spanning tree game on planar and bounded-treewidth graphs
TLDR
The Stackelberg Minimum Spanning Tree Game is a two-level combinatorial pricing problem played on a graph representing a network that is NP-hard on planar graphs but can be solved in polynomial time on graphs of bounded treewidth.
Origin-equivalence of two-way word transducers is in PSPACE
TLDR
It is proved that decidability can be equally recovered by adopting a slightly different, but natural semantics, called origin semantics, and introduced by Bojanczyk in 2014.
Application of logic to combinatorial sequences and their recurrence relations
TLDR
This paper presents a meta-analyses of the model Theoretic Interpretations of Counting Functions using LaSalle’s inequality as a model for solving the inequality of the following types: 1-2-3, 2-3-4, and 3-4-5.
...
...

References

SHOWING 1-10 OF 84 REFERENCES
The Monadic Second-Order Logic of Graphs VII: Graphs as Relational Structures
The Monadic Second-Order Logic of Graphs XI: Hierarchical Decompositions of Connected Graphs
Logical Description of Contex-Free Graph Languages
A graph language L is in the class C-edNCE of context-free edNCE graph languages if and only if L= f(T) where f is a partial function on graphs that can be defined in monadic second-order logic and T…
The monadic second-order logic of graphs XVI : Canonical graph decompositions
TLDR
It is established that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic and it is proved that the set of graphs having the same cycle matroid as a given 2-connected graph can be defined from this graph by Monadic second-Order formulas.
Logic, graphs, and algorithms
TLDR
An introduction into the theory underlying algorithmic meta theorems and a survey of the most important results in this area are presented.
Monadic Second-Order Logic, Graph Coverings and Unfoldings of Transition Systems
The Monadic Second-Order Logic of Graphs X: Linear Orderings
The Structure of Models of Decidable Monadic Theories of Graphs
  • D. Seese
  • Mathematics
    Ann. Pure Appl. Log.
  • 1991
The monadic second-order logic of graphs XV: On a conjecture by D. Seese
Circle graphs and monadic second-order logic
...
...