# 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…

## 14 Citations

Monadic Second-Order Logic for Graphs: Algorithmic and Language Theoretical Applications

- Computer ScienceLATA
- 2009

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

- Computer Science, Mathematics2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
- 2015

A new class of finite graph automata that recognize precisely the languages of finite graphs definable in monadic second-order logic is introduced.

An Auxiliary Logic on Trees: on the Tower-Hardness of Logics Featuring Reachability and Submodel Reasoning

- Philosophy, Computer ScienceFoSSaCS
- 2020

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

- MathematicsEur. J. Comb.
- 2011

Graph and Election Problems Parameterized by Feedback Set Numbers

- MathematicsArXiv
- 2011

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

- PhilosophyCICM Workshops
- 2013

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

- MathematicsJ. Comb. Optim.
- 2013

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

- Computer ScienceFSTTCS
- 2018

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

- MathematicsAMS-ASL Joint Special Session
- 2009

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.

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