| Project/Area Number |
08640065
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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 |
Algebra
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| Research Institution | Toho University |
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Principal Investigator |
KOBAYASHI Yuji Toho University, Faculty of Science, Professor, 理学部, 教授 (70035343)
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| Co-Investigator(Kenkyū-buntansha) |
UMEZU Yumiko Toho University, Faculty of Medicine, Associate Professor, 医学部, 助教授 (70185065)
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| Project Period (FY) |
1996 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1998: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1997: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1996: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | algebraic system / finite presentation / word problem / rewriting system / monoid / homotopy / homology / algebraic curve / ホモロジー / 決定問題 / 完備性 / cross-section / 自由モノイド / 正規言語 / 停止問題 |
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| Research Abstract |
We studied the word problem and other decision problems for finitely presented algebras by means of rewriting systems.
We found some relationship between the solvability of the word problem and the existence of complete rewriting systems with good properties in a language- theoretical sense for finitely presented monoids. We also studied cross-sections of monoids related to the above properties. For the word problem to be solvable, context-sensitive cross-sections suffice but context-free cross-sections do not (see [2] and [9]). We reported these results in a survey article [5].
We studied some important properties such as confluence and termination of rewriting systems themselves. In [6] we gave a result on the termination for confluent one-rule systems.
We showed that the rewriting techniques are useful too in the homotopy theory of the derivation graphs associated with monoid presentations. If a monoid has a complete homotopy reduction system, then it satisfies the homological finiteness property FP4. We always have the left canonical reduction system and it is complete if the presentation is nonspecial. These results are reported in [8].
We developed the method to construct a family of algebraic curves of genus g <greater than or equal> 2 with large rank modifying Neron's method
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