Monadic second-order evaluations on tree-decomposable graphs

Monadic Second-Order Evaluations on Tree-Decomposable Graphs

Every graph generated by a hyperedge replacement graph-grammar can be represented by a tree, namely the derivation tree of the derivation sequence that produced it. Certain functions on graphs can be computed recursively on the derivation trees of these graphs. By using monadic second-order logic and semiring homomorphisms, we describe in a single formalism a large class of such functions. Poly...

Monadic second-order model-checking on decomposable matroids

A notion of branch-width may be defined for matroids, which generalizes the one known for graphs. We first give a proof of the polynomial time model checking of MSOM on representable matroids of bounded branch-width, by reduction to MSO on trees, much simpler than the one previously known. We deduce results about spectrum of MSOM formulas and enumeration on matroids of bounded branch-width. We ...

Tree-structured Graphs and Monadic Second-order Logic

Space and circuit complexity of monadic second-order definable problemes on tree-decomposable structures

A famous theorem of Courcelle states that every problem that is definable in monadic second-order (mso) logic can be solved in linear time on input structures of bounded tree width. While Courcelle’s result is optimal from the algorithmic point of view, this thesis shows how to solve monadic secondorder definable decision, counting, and optimization problems on tree-widthbounded structures opti...

Circle graphs and monadic second-order logic

A circle graph is the intersection graph of a set of chords of a circle. If a circle graph is prime for the split (or join) decomposition defined by Cunnigham, it has a unique representation as a set of intersecting chords, and we prove that this representation can be defined by monadic second-order formulas. By using the (canonical) split decomposition of a circle graph, one can define in mona...