1996 Fiscal Year Final Research Report Summary
Synthetic Research on the Theory of Algorithms
| Project/Area Number |
06302013
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 総合 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
KOBAYASHI Kojiro Tokyo Institute of Technology Graduate School of Information Science and Technology Prof., 大学院・情報理工学研究科, 教授 (00016148)
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| Co-Investigator(Kenkyū-buntansha) |
MIYANO Satoru University of Tokyo Human Genome Center Prof., 医科学研究所, 教授 (50128104)
KANO Mikio Ibakaki University Faculty of Engineering Prof., 工学部, 教授 (20099823)
ENOMOTO Hikoe Keio University Department of Science and Engineering Prof., 理工学部, 教授 (00011669)
IGARASHI Shigeru University of Tsukuba Institute of Information Sciences Prof., 電子情報工学系, 教授 (80027367)
ARIKAWA Setsuo Kyushu University Graduate School of Information Science and Electrical Engineer, 大学院・システム情報科学研究科, 教授 (40037221)
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| Project Period (FY) |
1994 – 1996
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| Keywords | Identification of Differential Equations / Knowledge Propositional Logic / Algebraic Semantics / Relational Algebra / Verification of Programs / Temporal Logic / Structure of Proteins / Music Information Processing |
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| Research Abstract |
1. Theory of Algorithms : A framework for developing a theory of numerical computation based on the theory of algorithms was proposed. A method to identify a differential equation from observed numerical data of behavior of a physical system obeying the equation was shown. This method corrects the weakness of the usual one concerning the increase of sizes of intervals resulting from division. 2. Logic and Algorithms : A normal form theorem for the knowledge propositional logic was obtained. Some results that show the usefulness and the limitation of algebraic semantics for nonclassical propositional logic were obtained. The relational calculus and the relational algebra have been sncessfully applied to formulate and analyze several basic notions in computer science such as nondeterministic processes, knowledge base systems, graph rewriting systems, and so on. 3. Programming Languages and Models of Computation : Several formal systmes for analyzing the behavior of parallel programs have been proposed. In one of them, the envelope theory, we can analyze the behavior of parallel programs more naturally than in the usual temporal logic. 4. Algorithms and their Complexity : A new tree structure for representing systax of sentences has been proposed and an English to Japanese translation system based on this tree structure was developed. One method for visualizing music expression in an object oriented environment has been proposed. A hypergraph representation of structures of proteins that captures their tertiary structures in loose way has been proposed. Using this representaion, conformation rules can be formulated as graph rewriting rules, and a PAC learning algorithm has been discovered for a class of conformations. It has been shown that the class of edge-magic graphs cannot be characterized with inhibiting subgraphs.
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