Abstract
We introduce various types of top-down pushdown infinite tree automata. We extend the Landweber-Staiger-Wagner hierarchy to pushdown infinite tree automata. We prove that the extension of Kleene’s theorem to pushdown infinite tree automata is not possible. We characterize recognizable (i.e. regular) infinite trees and extend Eilenberg’s theorem to ω-tree pushdown automata. We give some characterizations of infinite computations of nondeterministic context-free program schemes. We show that the equivalence problem for nondeterministic context-free program schemes is unsolvable.
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