  A vertex-subset graph problem $Q$ defines which subsets of the vertices of an
input graph are feasible solutions. The reconfiguration version of a
vertex-subset problem $Q$ asks whether it is possible to transform one feasible
solution for $Q$ into another in at most $\ell$ steps, where each step is a
vertex addition or deletion, and each intermediate set is also a feasible
solution for $Q$ of size bounded by $k$. Motivated by recent results
establishing W[1]-hardness of the reconfiguration versions of most
vertex-subset problems parameterized by $\ell$, we investigate the complexity
of such problems restricted to graphs of bounded treewidth. We show that the
reconfiguration versions of most vertex-subset problems remain PSPACE-complete
on graphs of treewidth at most $t$ but are fixed-parameter tractable
parameterized by $\ell + t$ for all vertex-subset problems definable in monadic
second-order logic (MSOL). To prove the latter result, we introduce a technique
which allows us to circumvent cardinality constraints and define
reconfiguration problems in MSOL.
