1998 Fiscal Year Final Research Report Summary
Mathematical study of Constructive Concurrent and Distributed Programm system
| Project/Area Number |
09640302
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ritsumeikan University |
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Principal Investigator |
TAKAYAMA Yukihide Faculty of Science and Engneering Ritsumeikan University, Associate Professor, 理工学部, 助教授 (20247810)
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| Co-Investigator(Kenkyū-buntansha) |
NARUKI Isao Faculty of Science and Engneering Ritsumeikan University, Professor, 理工学部, 教授 (90027376)
DOI Koji Faculty of Science and Engneering Ritsumeikan University, Professor, 理工学部, 教授 (20025290)
IKEDA Nobuyuki Faculty of Science and Engneering Ritsumeikan University, Professor, 理工学部, 教授 (00028078)
HARA Keisuke Faculty of Science and Engneering Ritsumeikan University, Lecturer, 理工学部, 講師 (30298715)
SATO Yosuke Faculty of Science and Engneering Ritsumeikan University, Professor, 理工学部, 教授 (50257820)
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| Project Period (FY) |
1997 – 1998
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| Keywords | constructive programming / concurrency theory / computer algebra |
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| Research Abstract |
First of all, we developed a prototype of linear logic prover system, which is a subsystem of our Rits Concurrency Workbench - an experimental programming system based on pi calculus and Linear Logic. Also, we fixed a final version of the theory of concurrency analysis based on homotopy model of concurrent computation.
For computer algebra, we improved efficiency of our set constraint solver system by refining algorithms in the program and developed a prototype GUI system for displaying the set constraint. Also, we found a drastically new method for parallelize the Boolean Gr6bner basis algorithm, which is the core part of the set constraing solver, and carried out implementation in two different programming languages, KLIC and Asir. Based on this idea, we triecl to find parallelized algorithm of Grobner basis for von neumann regular ring, which is an extension of Boolean Grobner basis.
Finally, we obtained an interesting result relating both to concurrent programming and computer algebra. By using combinatorial commutative ring theory and algebraic topology, we founci an effective method for checking Cohen-Macaulayness of a simplicial complex by analysing the 1-skeleton of the complex. This result has close relation with partially ordered set, which is useful for modeling structure of concurrent computation.
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