# bounded tree width

## Complexity of QBF(Bounded Treewidth) ★★

Author(s): Moshe Y. Vardi

**Question**What is the computational complexity of QBF(Bounded Treewidth)? Is it PSPACE-complete? In PTIME?

Keywords: bounded tree width; Computational Complexity; FMT12-LesHouches; QBF

## Monadic second-order logic with cardinality predicates ★★

Author(s): Courcelle

The problem concerns the extension of Monadic Second Order Logic (over a binary relation representing the edge relation) with the following atomic formulas:

- \item \item

where is a fixed recursive set of integers.

Let us fix and a closed formula in this language.

**Conjecture**Is it true that the validity of for a graph of tree-width at most can be tested in polynomial time in the size of ?

Keywords: bounded tree width; cardinality predicates; FMT03-Bedlewo; MSO