Clones of manyvalued logic functions (esp.semirigidity problems)
Project/Area Number  08680383 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
計算機科学

Research Institution  Tsukuba College of Technology 
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)

CoInvestigator(Kenkyūbuntansha) 
POGOSYAN Grant International Christian University Professor, 理学科, 教授 (90234640)

Project Period (FY) 
1996 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1998 : ¥400,000 (Direct Cost : ¥400,000)
Fiscal Year 1997 : ¥300,000 (Direct Cost : ¥300,000)

Keywords  manyvalued logic / clone / antichain / intersecting antichain / clique / permutation / autodual functions / ncube / 単調関数 / 交差関係 / 数え上げ / intersecting antichain 
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 ncube. 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 11 correspondence between the set of intersecting antichains in the lowerhalf of the ncube and the set of intersecting antichains in the (n1)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 problemfully solved only for *A*=2, 3one 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)quasilinear 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)

Report
(4results)
Research Products
(11results)