Abstract
In this paper two complexity measures are investigated for the class of deterministic tree-walking transducers. We show that, when a constant bound is imposed on the crossing number of these devices, the rank of the input tree language induces an infinite, non-collapsing hierarchy. Using this result we solve some language-theoretic questions that were left open in the literature. Our separation result can also be transferred to other classes in the family of finite copying parallel rewriting systems, since a weak equivalence relation holds between these classes and deterministic tree-walking transducers, even when the complexity measures above are bounded.
We are grateful to Joost Engelfriet and Ryuichi Nakanisi for helpful discussion on topics related to this paper. This research was conducted while the second author was a post-doctoral fellow at the Institute for Research in Cognitive Science at the University of Pennsylvania. The research was sponsored by the following grants: ARO DAAL 03-89-C-0031; DARPA N00014-90-J-1863; NSF IRI 90-16592; and Ben Franklin 91S.3078C-1.
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Rambow, O., Satta, G. (1994). A rank hierarchy for deterministic tree-walking transducers. In: Tison, S. (eds) Trees in Algebra and Programming — CAAP'94. CAAP 1994. Lecture Notes in Computer Science, vol 787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017490
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DOI: https://doi.org/10.1007/BFb0017490
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