Deterministic tree pushdown automata and monadic tree rewriting systems☆

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Abstract

We show that the deterministic tree pushdown automata of J. H. Gallier and R. V. Book (Theoret. Comput. Sci.37 (1985), 123–150) are strictly more powerful than the corresponding automata of K. M. Schimpf (Ph. D. dissertation, University of Pennsylvania, 1982). In fact, even one of the additional features of the former automata, the capability to delete or to duplicate subtrees of the tree stack increases the recognition power. Also we show that finite unions of congruence classes of canonical monadic tree rewriting systems can be recognized by deterministic tree pushdown automata without the additional acceptance conditions used in op. cit. For right-linear monadic tree rewriting systems the same is true for unions of congruence classes over regular tree languages.

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This research was performed while the author was visiting the Department of Mathematics, University of California, Santa Barbara. It was supported in part by the Academy of Finland, the ASLA/Fulbright Foundation, and by the National Science Foundation under Grant DCR8314977.

Copyright © 1988 Published by Elsevier Inc.