Abstract
Tree transducers may be used to perform symbolic computations. A function f from one algebra into another is computed by a transduction that yields for any term t representing an element a a term t′ representing f(a). We consider the case where the input algebra is a term algebra, the target algebra is given by the natural numbers with operations ⊔, +, ·, and f is injective. In this case f may be seen as a coding of terms as natural numbers. It is shown that functions computed by deterministic top-down tree transducers cannot compress totally balanced trees: The binary representation of f(t) is at least as long as t up to a constant factor.
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References
B.S. Baker. Composition of top-down and bottom-up tree transductions. Information and Control 41, 186–213, 1979.
B. Courcelle, M. Mosbah. Monadic second order evaluations on treedecomposable graphs. Theoretical Computer Science 109, 49–82, 1993.
F. Drewes. A lower bound on the growth of functions computed by tree transducers. Report 4/93, Univ. Bremen, 1993.
F. Drewes. Transducibility — symbolic computation by tree-transductions. Report 2/93, Univ. Bremen, 1993.
J. Engelfriet. Bottom-up and top-down tree transformations — a comparison. Mathematical Systems Theory 9(3), 198–231, 1975.
J. Engelfriet. Some open questions and recent results on tree transducers and tree languages. In R.V. Book, editor, Formal Language Theory: Perspectives and Open Problems, 241–286. Academic Press, New York, 1980.
F. Gécseg, M. Steinby. Tree Automata. Akadémiai Kiadó, Budapest, 1984.
A. Habel, H.-J. Kreowski, W. Vogler. Decidable boundedness problems for sets of graphs generated by hyperedge-replacement. Theoretical Computer Science 89, 33–62, 1991.
C.St.J.A. Nash-Williams. On well-quasi-ordering trees. In Proc. Cambridge Phil. Soc. 59, 833–835, 1963.
H. Seidl. Finite tree automata with cost functions. In J.-C. Raoult, editor, Proc. CAAP 92, Lecture Notes in Computer Science 581, 279–299, 1992.
E. Wanke. On the decidability of integer subgraph problems on context-free graph languages. In L. Budach, editor, Proc. Fundamentals of Computation Theory, Lecture Notes in Computer Science 529, 415–426, 1991.
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© 1994 Springer-Verlag Berlin Heidelberg
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Drewes, F. (1994). A lower bound on the growth of functions computed by tree transductions. 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/BFb0017476
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DOI: https://doi.org/10.1007/BFb0017476
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