1998 Fiscal Year Final Research Report Summary
Clones of many-valued logic functions (esp.semirigidity problems)
| Project/Area Number |
08680383
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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 | Tsukuba College of Technology |
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Principal Investigator |
MIYAKAWA Masahiro Div.for the Visually Impaired, Computer Professor Science Dept.Professor, 視覚部情報処理学科, 教授 (70248748)
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| Co-Investigator(Kenkyū-buntansha) |
POGOSYAN Grant International Christian University Professor, 理学科, 教授 (90234640)
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| Project Period (FY) |
1996 – 1998
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| Keywords | many-valued logic / clone / antichain / intersecting antichain / clique / permutation / autodual functions / n-cube |
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| Research Abstract |
1. We gave an explicit formula for the number of clique (or intersecting) Boolean functions in terms of the parameters based upon the number of intersecting antichains in the lower half of the n-cube. We obtained the numbers of clique functions up to seven variables through computer evaluations of the parameter. (Reference 1)
2. We proved that there is a 1-1 correspondence between the set of intersecting antichains in the lower-half of the n-cube and the set of intersecting antichains in the (n-1)-cube. This reduces the enumeration of intersecting antichains contained in the former set to that in the latter. (Reference 2)
3. The study of semirigid sets arose from the classification of bases. In this complex problem-fully solved only for *A*=2, 3-one of the tasks is to find all minimal nontrivial intersections of systems of maximal clones. Most of the clones are determined by reflexive relations (binary or of higher arities) and so we need to determine subsets R of these relations such that every function preserving all relations in R is either constant or is a projection. In this paper we give a short overview of this problem for 1) isotone relations, 2) central relations and 3)quasi-linear relations. Finally we add some new results for 4) autodual clones ; we proved that for k prime the foundations of every two maximal autodual clones are rigid, i.e. they share only the identity map. (Reference 3)
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