  A strong backdoor in a formula $\phi$ of propositional logic to a tractable
class $\mathcal{C}$ of formulas is a set $B$ of variables of $\phi$ such that
every assignment of the variables in $B$ results in a formula from
$\mathcal{C}$. Strong backdoors of small size or with a good structure, e.g.
with small backdoor treewidth, lead to efficient solutions for the
propositional satisfiability problem SAT. In this paper we propose the new
notion of recursive backdoors, which is inspired by the observation that in
order to solve SAT we can independently recurse into the components that are
created by partial assignments of variables. The quality of a recursive
backdoor is measured by its recursive backdoor depth. Similar to the concept of
backdoor treewidth, recursive backdoors of bounded depth include backdoors of
unbounded size that have a certain treelike structure. However, the two
concepts are incomparable and our results yield new tractability results for
SAT.
