Studies on representation-based computational structures of spaces and figures, and on related structures like fractals

2014 Fiscal Year Final Research Report

• Project/Area Number: 22500014
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: Kyoto University
• Principal Investigator: TSUIKI Hideki 京都大学, 人間・環境学研究科(研究院), 教授 (10211377)
• Research Collaborator: 山田 修司 京都産業大学, 理学部, 教授 ; 大田 春外 静岡大学, 教育学部, 教授 ; 竹内 泉 産業技術総合研究所, 研究員 ; 塚本 靖之 京都大学, 人間・環境学研究科 ; 寺山 慧 京都大学, 人間・環境学研究科
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 実数計算 / ドメイン理論 / 位相空間論 / 力学系

Outline of Final Research Achievements

Gray-code embedding is a representation of real numbers with sequences containing bottoms and an IM2 machine is a machine which operates on bottomed sequences. Proper dyadic subbase is a generalization of Gray-code embedding to topological spaces. We studied domain structures which correspond to finite states of IM2-machines that operate according to dyadic subbases. We also studied exact full-folding maps which are dynamical systems that derive proper dyadic subbases, and a stream calculus which input and output Gray-code embedding.

Free Research Field

理論計算機科学