Download graph structure and monadic secondorder logic. This tutorial will present an overview of the use of monadic secondorder logic to describe sets of finite graphs and graph transfor mations, in relation with the notions of treewidth and clique. Separately the properties of graphs can be studied in a logical language called monadic secondorder logic. The domain of the structure representing a graph is the set of. A graph can also be considered as a logical structure of a certain type. Language theoretical aspects, graph structure,is a flexible concept,covering,many,differ ent types of graph,properties. Hierarchical decompositions yielding the notions of treewidth and. Graph query verification using monadic secondorder logic. In mathematical logic, monadic secondorder logic mso is the fragment of secondorder logic where the secondorder quantification is limited to quantification over sets.
Pdf graph structure and monadic secondorder logic a. Graph structure and monadic secondorder logic by bruno. A graph language l is in the class cednce of contextfree ednce graph languages if and only if l ft where f is a function on graphs that can be defined in monadic secondorder logic and t is. The study of graph structure has advanced in recent years with great strides. Pdf on jun 14, 2012, bruno courcelle and others published graph structure and monadic secondorder logic. Graphs can be described by relational structures, i. Hierarchical decompositions yielding the notions of treewidth and cliquewidth, expressed by terms written with appropriate graph operations and associated with monadic secondorder logic are important tools for the construction of fixedparameter tractable algorithms and also for the extension of methods and results of formal language theory to the description of sets of finite graphs. Cambridge core programming languages and applied logic graph structure and monadic secondorder logic by bruno courcelle. Graph structure is a flexible concept covering many different types of graph properties. Graph structure and monadic secondorder logic labri. This informal overview presents the main definitions, results and open problems and tries to answer some. Request pdf on sep 18, 2012, bruno courcelle and others published graph structure and monadic secondorder logic find, read and cite all the research you need on researchgate.
It is particularly important in the logic of graphs, because of courcelles theorem, which provides algorithms for evaluating monadic secondorder formulas over graphs of bounded treewidth. Monadic secondorder logic and its use for expressing graph properties. In this book, these two features of graph structure. Graph structure and monadic secondorder logic request pdf. Graph structure and monadic secondorder logic by bruno courcelle. Bruno courcelle, joost engelfriet to cite this version. Graph structure and monadic secondorder logic, a language. A languagetheoretic approach find, read and cite all the research you need on.