tailieunhanh - Some properties of the positive boolean dependencies in the database model of block form

The report proposes the concept of positive boolean dependency in the database model of block form, proving equivalent theorem of three derived types, necessary and sufficient criteria of the derived type, the member problem. In addition, some properties related to this concept in the case of block r degenerated into relation are also expressed and demonstrated here. | Journal of Computer Science and Cybernetics, , (2015), 159–169 DOI: SOME PROPERTIES OF THE POSITIVE BOOLEAN DEPENDENCIES IN THE DATABASE MODEL OF BLOCK FORM TRAN MINH TUYEN1 , TRINH DINH THANG2 , AND NGUYEN XUAN HUY3 1 Vietnam Trade Union University; tuyentm@ Pedagogical University No. 2; thangsp2@ 3 Institute of Information Technology, Vietnam Academy of Science and Technology; nxhuy564@ 2 Hanoi Abstract. The report proposes the concept of positive boolean dependency in the database model of block form, proving equivalent theorem of three derived types, necessary and sufficient criteria of the derived type, the member problem. In addition, some properties related to this concept in the case of block r degenerated into relation are also expressed and demonstrated here. Keywords. Positive boolean dependence, block, block scheme. 1. . THE DATABASE MODEL OF BLOCK FORM The block, slice of the block Definition ( [1]) Let R = (id; A1 , A2 , . . . , An ) be a finite set of elements, where id is non-empty finite index set, Ai (i = 1 . . . n) is the attribute. Each attribute Ai (i = 1 . . . n) there is a corresponding value domain dom (Ai ). A block r on R, denoting r(R) consists of a finite number of elements that each element is a family of mappings from the index set id to the value domain of the attributes Ai (i = 1 . . . n). t ∈ r(R) ⇔ t = {ti : id → dom(Ai )}i=1n . The block denotes r(R) or r(id; A1 , A2 , . . . , An ), sometimes without fear of confusion it simply denotes r. Definition ( [1]) Let R = (id; A1 , A2 , . . . , An ), r(R) is a block over R. For each x ∈ id, r(Rx ) denotes a block with Rx = ({x}; A1 , A2 , . . . , An ), such is: tx ∈ r(Rx ) ⇔ tx = {ti = ti }i=1n , t ∈ r(R), t = {ti : id → dom(Ai )}i= , x x where ti (x) = ti (x), i = 1 . . . n. x Then r(Rx ) is called a slice of block r(R) at point x. . Functional dependencies Here for simplicity, the following .