Monadic second-order logic, graph coverings and unfoldings of transition systems

Monadic Second-Order Logic, Graph Coverings and Unfoldings of Transition Systems

We prove that every monadic second-order property of the unfolding of a transition system is a monadic second-order property of the system itself. An unfolding is an instance of the general notion of graph covering. We consider two more instances of this notion. A similar result is possible for one of them but not for the other.

Graph structure and Monadic second-order logic

Exclusion of minor, vertex-minor, induced subgraph Tree-structuring Monadic second-order logic : expression of properties, queries, optimization functions, number of configurations. Mainly useful for tree-structured graphs (Second-order logic useless) Tools to be presented Algebraic setting for tree-structuring of graphs Recognizability = finite congruence ≡ inductive computability ≡ finite det...

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

Graph structure is 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 Logic are important tools for the construction of Fixed-Parameter Tractable algorithms and also for the extension of methods ...

Bruno Courcelle Graph Structure and Monadic Second - Order Logic

Graph-Query Verification using Monadic Second-Order Logic

This paper presents a static verification algorithm for a core subset of UnCAL, the query algebra for graph-structured databases proposed by Bunemann et al. Given a query and input/output schemas, our algorithm statically verifies that any graph satisfying the input schema is converted by the query to a graph satisfying the output schema. The basic idea is to reformulate the semantics of UnCAL ...