Complexity Theory of (Functions on) Compact Metric Spaces

Akitoshi Kawamura, Florian Steinberg, Martin Ziegler

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

5 被引用数 (Scopus)

抄録

We promote the theory of computational complexity on metric spaces: as natural common generalization of (i) the classical discrete setting of integers, binary strings, graphs etc. as well as of (ii) the bit-complexity theory on real numbers and functions according to Friedman, Ko (1982ff), Cook, Braverman et al.; as (iii) resource-bounded refinement of the theories of computability on, and representations of, continuous universes by Pour-El&Richards (1989) and Weihrauch (1993ff); and as (iv) computational perspective on quantitative concepts from classical Analysis: Our main results relate (i.e. upper and lower bound) Kolmogorov's entropy of a compact metric space X polynomially to the uniform relativized complexity of approximating various families of continuous functions on X. The upper bounds are attained by carefully crafted oracles and bit-cost analyses of algorithms perusing them. They all employ the same representation (i.e. encoding, as infinite binary sequences, of the elements) of such spaces, which thus may be of own interest. The lower bounds adapt adversary arguments from unit-cost Information-Based Complexity to the bit model. They extend to, and indicate perhaps surprising limitations even of, encodings via binary string functions (rather than sequences) as introduced by Kawamura&Cook (SToC'2010, 3.4). These insights offer some guidance towards suitable notions of complexity for higher types.

本文言語英語
ホスト出版物のタイトルProceedings of the 31st Annual ACM-IEEE Symposium on Logic in Computer Science, LICS 2016
出版社Institute of Electrical and Electronics Engineers Inc.
ページ837-846
ページ数10
ISBN(電子版)9781450343916
DOI
出版ステータス出版済み - 7 5 2016
外部発表はい
イベント31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2016 - New York, 米国
継続期間: 7 5 20167 8 2016

出版物シリーズ

名前Proceedings - Symposium on Logic in Computer Science
Proceedings - Symposium on Logic in Computer Science
ISSN(印刷版)1043-6871

その他

その他31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2016
Country米国
CityNew York
Period7/5/167/8/16

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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