Abstract
In order to investigate the structure of computable functions over (binary) trees, we define two classes of recursive tree functions by extending the notion of recursive functions over natural numbers in two different ways, and also define the class of functions computable by whileprograms over trees. Then we show that those classes coincide with the class of conjugates of recursive functions over natural numbers via a standard coding function (between trees and natural numbers). We also study what happens when we change the coding function, and present a necessary and sufficient condition for a coding function to satisfy the property above mentioned.
Present address: Compaq Computer K. K., Tokyo 167-8533 Japan. E-mail: Masahiro.Kimoto@jp.compaq.com
Present address: Department of Information Science, International Christian University, Tokyo 181-8585 Japan. E-mail: mth@icu.ac.jp
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
W. S. Brainerd and L. H. Landweber (1974). Theory of Computation, John Wiley & Sons.
S. Eilenberg and C. C. Elgot (1970). Recursiveness, Academic Press.
M. Kimoto (2000). On Computability of Functions over Binary Trees, Master Thesis, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology.
D. E. Knuth (1973). The Art of Computer Programming, Vol.1 — Fundamental Algorithms, Addison Wesley.
H. E. Rose (1984). Subrecursion — Functions and Hierarchies, Clarendon Press, Oxford.
M. Takahashi (1998). A primer on proofs and types, Theories of Types and Proofs, MSJ-Memoirs Vol.2 (M. Takahashi, M. Okada, and M. Dezani, eds., Mathematical Society of Japan), pp.1–44.
M. Takahashi (to appear). Lambda-representable functions over term algebras, International Journal of Foundations of Computer Science.
J. V. Tucker and J. I. Zucker (to appear). Computable functions and semicomputable sets on many-sorted algebras, Handbook of Logic in Computer Science, Vol.5 (S. Abramsky, D. M. Gabbay and T. S. E. Maibaum, eds., Oxford University Press).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kimoto, M., Takahashi, M. (2000). On Computable Tree Functions. In: Jifeng, H., Sato, M. (eds) Advances in Computing Science — ASIAN 2000. ASIAN 2000. Lecture Notes in Computer Science, vol 1961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44464-5_20
Download citation
DOI: https://doi.org/10.1007/3-540-44464-5_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41428-5
Online ISBN: 978-3-540-44464-0
eBook Packages: Springer Book Archive