Courcelle, Bruno

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 ?