FO model checking on nested pushdown trees

Abstract

Nested Pushdown Trees are unfoldings of pushdown graphs with an additional jump-relation. These graphs are closely related to collapsible pushdown graphs. They enjoy decidable μ-calculus model checking while monadic second-order logic is undecidable on this class. We show that nested pushdown trees are tree-automatic structures, whence first-order model checking is decidable. Furthermore, we prove that it is in 2-EXPSPACE using pumping arguments on runs of pushdown systems. For these arguments we also develop a Gaifman style argument for graphs of small diameter. © 2009 Springer Berlin Heidelberg.