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Recently we proved that first-order model checking on nested pushdown trees can be done in doubly exponential alternating time with linearly many alternations. Using the interpretation method of Compton and Henson we give a matching lower bound, i.e., we prove that first-order model checking on nested pushdown trees is complete for ATIME(exp2(cn), cn) with respect to log-lin reductions.

First-Order Model Checking on Nested Pushdown Trees is Complete for Doubly Exponential Alternating Time