Workshop on Logic, Graph Transformations, Finite and Infinite Structures

Abstract

Like in Barcelona in 2002, a satellite workshop will be organized during one day and a half.

Its main topics are the use of logic for representing graph properties and graph transformations, and the definition and the study of hierarchical structurings of graphs, in order to obtain decidability results and polynomial time algorithms. The two main motivations for this type of study are the construction of efficient algorithms for particular types of graphs and the verification of programs based on infinite graphs representing all possible computations. In many cases, the properties to verify are specified in certain logical languages. It is thus important to understand the relationships between the logical expression of properties (graph properties or properties of programs) and the complexity of their verification. This is the aim of Descriptive Complexity. The possibility of constructing logical formulas in the powerful but nevertheless restricted language of Monadic Second-Order Logic is frequently based on deep combinatorial properties. The Graph Minor Theorem and its extensions to Matroids and related notions like Isotropic Systems have a prominent place among such properties. They are linked to tree-decompositions and similar hierarchical decompositions. Other notions of hierarchical structuring like modular and split decompositions are also recognized as important. Among the numerous notions of graph structuring proposed by graph theoreticians, some fit better with logic and algorithmics. It is thus interesting to revisit these notions in a logical and algorithmic perspective.