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.
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Kartzow, A. (2009). FO Model Checking on Nested Pushdown Trees. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_39
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DOI: https://doi.org/10.1007/978-3-642-03816-7_39
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