1997 Fiscal Year Final Research Report Summary
A Study of the complete Problems for Low-Level Complexity Classes
| Project/Area Number |
07680344
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
計算機科学
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
KASAI Takumi The University of Electro-Communications, Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (70027382)
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| Co-Investigator(Kenkyū-buntansha) |
TANI Sei'ichi Tokai University, Faculty of Science, Lectrer, 理学部, 講師 (70266708)
YAMAZAKI Koichi Gunma University, Faculty of Engineering, Lecturer, 工学部, 講師 (00246662)
IWATA Shigeki Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (80102028)
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| Project Period (FY) |
1995 – 1997
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| Keywords | Complexity / Complete Problems / Approximation Algoritms / Formal Language / Language Processing / Graph Algoritms / Graph Isomorphism / Merging Network |
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| Research Abstract |
We concern some basic properties of the complete problems with low level complexity. For a variety of discrete problems, we develop the efficient algorithm of them, and analyze the class of the algorithms qualitatively and quantitatively.
Dr.Kasai, the head investigator, formalized various problems in the natural language processing. He introduced a notion for the new expression model of sentence structural trees called "left-right tree", and discussed the class of parsing algorithms. He also concerned the language transformational theory and formalized the class of bi-stage transducer. Transformations of languages are generally formalized by a chain of executions of tree automaton that transform trees into trees. We proveed that any chain of executions of tree automaton is realized by one execution of a bi-stage transducer. This result is applicable to not only natural language processing but also numerical formula processing and many others.
Dr.Iwata studied the lower bounds of the number of comparators in merging networks. He theoretically proved that M (6,6)=17, which had been unknown. He also proved M (4,5)=12, M (4,6)=14, M (4,7) =16, M (4,8) =17 and M (5,6) =16 by computer computation with efficient algorithms.
Dr.Yamazaki analyzed graph algorithms. It is an important open question whether there exists an algorithm with O (f (k) n^c) running time for isomorphism testing of graphs of bounded degree (or treewidth), where k is the upper bound and c is a constant and independent of k.Yamazaki et al.have presented O (f (k) n^c) time algorithm for a subclass of graphs of bounded degree (or treewidth). They also showed that it is hard to know when Greedy algorithm is good for finding independent sets.
Dr.Tani analyzed the number of questions in PAC-learning.
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