没有安装node对等点依赖_功能依赖项的对等数据库管理系统

没有安装node对等点依赖

Equivalence of Functional dependencies states that, if the relations of different Functional dependencies sets are given, then we have to find out whether one Functional dependency set is a subset of other given set or both the sets are equal.

功能依赖项的等价性指出，如果给出了不同功能依赖项集的关系，则我们必须找出一个功能依赖项集是其他给定集的子集还是两个集相等。

To find out whether one Functional dependency set is a subset of other given set or both the sets are equal.

找出一个功能依赖集是另一个给定集的子集还是两个集相等。

Suppose R1 and R2 are two Functional dependencies sets for a relation R.

假设R1和R2是关系R的两个功能依赖集。

If all Functional dependencies of R1 can be derived from Functional dependencies present in R2, we can say that R2 is a subset of R1 (R2 ⊃ R1).
如果可以从R2中存在的功能依赖性中得出R1的所有功能依赖性，则可以说R2是R1的子集(R2 = R1) 。
If all Functional dependencies of R2 can be derived from Functional dependencies present in R1, we can say that R1 is a subset of R2 (R1 ⊃ R2).
如果R2的所有功能相关性都可以从R1中存在的功能相关性中得出，则可以说R1是R2的子集(R1⊃R2) 。
If 1 and 2 both are satisfied, then R1 = R2.
如果1和2都满足，则R1 = R2 。

情况1)确定是否为R2⊃R1 (Case 1) Determining Whether R2 ⊃ R1 or not)

Steps are followed to determine whether R2 is a subset of R1 (R2 ⊃ R1) or not,

遵循步骤确定R2是否是R1的子集(R2⊃R1)，

Step 1)

第1步)

Take into consideration, the functional dependencies of set R1.
考虑到集合R1的功能依赖性。
For every functional dependency P→ Q, find by using the functional dependencies of set R1, the closure of P.
对于每个功能依赖项P→Q，通过使用集合R1的功能依赖关系来查找P的闭包。

Step 2)

第2步)

Take into consideration, the functional dependencies of set R2.
考虑到集合R2的功能依赖性。
For every functional dependency P→ Q, find by using the functional dependencies of set R2, the closure of P.
对于每个功能依赖项P→Q，使用集合R2的功能依赖关系来查找P的闭包。

Step 3)

步骤3)

Compare the results of Step 1 and Step 2.
比较步骤1和步骤2的结果。
If the functional dependency of set R2 has determined all those attributes that were determined by the functional dependencies of set R1, then it means R2 ⊃ R1.
如果集合R2的功能依赖性确定了所有由集合R1的功能依赖性确定的属性，则意味着R2 = R1。
Thus, we conclude R2 is a subset of R1 (R2 ⊃ R1) otherwise not.
因此，我们得出结论：R2是R1的子集(R2 = R1)，否则不是。

情况2)确定是否R1⊃R2 (Case 2) Determining Whether R1 ⊃ R2 or not)

Steps are followed to determine whether R1 is a subset of R2 (R1 ⊃ R2),

遵循步骤确定R1是否为R2的子集(R1⊃R2)，

Step 1)

第1步)

Take into consideration the functional dependencies of set R2.
考虑集合R2的功能依赖性。
For every functional dependency P → Q, find by using the functional dependencies of set R2, the closure of P.
对于每个功能依赖项P→Q，通过使用集合R2的功能依赖关系来查找P的闭包。

Step 2)

第2步)

Take into consideration the functional dependencies of set R1.
考虑集合R1的功能依赖性。
For every functional dependency P → Q, find by using the functional dependencies of set R1, the closure of P.
对于每个功能依赖项P→Q，通过使用集合R1的功能依赖关系来查找P的闭包。

Step 3)

步骤3)

Compare the results of Step 1 and Step 2.
比较步骤1和步骤2的结果。
If the functional dependency of set R1 has determined all those attributes that were determined by the functional dependencies of set R2, then it means R1 ⊃ R2.
如果集合R1的功能依赖性确定了所有由集合R2的功能依赖性确定的属性，则意味着R1 R R2。
Thus, we conclude that R1 is a subset of R2 (R1 ⊃ R2) otherwise not.
因此，我们得出结论，R1是R2的子集(R1⊃R2)，否则不是。

情况3)确定R1和R2是否彼此满足 (Case 3) Determining Whether Both R1 and R2 satisfy each other or not)

If R2 is a subset of R1 and R1 is a subset of R2, then both R1 and R2 satisfied each other.
如果R2是R1的子集，而R1是R2的子集，则R1和R2彼此满足。
Thus, if both the above cases satisfied, we conclude that R1 = R2.
因此，如果以上两种情况都满足，我们可以得出R1 = R2。

基于功能依赖项等效性的示例 (Example based on Equivalence of Functional Dependencies)

Q) A relation R (P, Q, U, S, and T) is having two functional dependencies sets R1 and R2, which is shown as

Q)关系R(P，Q，U，S和T)具有两个功能依赖项集R1和R2，显示为

    Set R1:         Set R2:
P → C           P → QU
PQ → U          S → PT
S → T

Solution...

解...

Case 1) Determining Whether R2 ⊃ R1 or not

情况1)确定是否为R2⊃R1

Step 1)

第1步)

(P)+ = {P, Q, U} // closure of left side of P → QU using set R1.
(P)+ = {P，Q，U} //使用集合R1关闭P→QU的左侧。
(S)+ = {P, Q, U, S, T} // closure of left side of S → PT using set R1.
(S)+ = {P，Q，U，S，T} //使用集合R1关闭S→PT的左侧。

Step 2)

第2步)

(P)+ = {P, Q, U} // closure of left side of P → QU using set R2.
(P)+ = {P，Q，U} //使用集合R2关闭P→QU的左侧。
(S)+ = {P, Q, U, S, T} // closure of left side of S → PT using set R2.
(S)+ = {P，Q，U，S，T} //使用集合R2关闭S→PT的左侧。

Step 3)

步骤3)

Comparing the results of Step 1 and Step 2, we find,

比较步骤1和步骤2的结果，我们发现，

Functional dependencies of set R2 can determine all the attributes which have been determined by the functional dependencies of set R1.
集合R2的功能依赖性可以确定由集合R1的功能依赖性确定的所有属性。
Thus, we conclude R2 is a subset of R1 i.e. R2 ⊃ R1.
因此，我们得出结论，R2是R1的子集，即R2 = R1。

Case 2) Determining Whether R1 ⊃ R2 or not

情况2)确定是否R1⊃R2

Step 1)

第1步)

(P)⁺ = {P, Q, U} // closure of left side of P→ Q using set R2.
(P) ⁺ = {P，Q，U} //使用集合R2关闭P→Q的左侧。
(PQ)⁺ = {P, Q, U} // closure of left side of PQ → U using set R2.
(PQ) ⁺ = {P，Q，U} //使用集合R2关闭PQ→U的左侧。
(S)⁺ = {P, Q, U, S, T} // closure of left side of S → PU and S → T using set R2.
(S) ⁺ = {P，Q，U，S，T} //使用集合R2关闭S→PU和S→T的左侧。

Step 2)

第2步)

(P)⁺ = {P, Q, U} // closure of left side of P→ Q using set R1.
(P) ⁺ = {P，Q，U} //使用集合R1关闭P→Q的左侧。
(PQ)⁺ = {P, Q, U} // closure of left side of PQ → U using set R1.
(PQ) ⁺ = {P，Q，U} //使用集合R1关闭PQ→U的左侧。
(S)⁺ = {P, Q, U, S, T} // closure of left side of S → PU and S → T using set R1.
(S) ⁺ = {P，Q，U，S，T} //使用集合R1关闭S→PU和S→T的左侧。

Step 3)

步骤3)

Comparing the results of Step 1 and Step 2, we find,

比较步骤1和步骤2的结果，我们发现，

Functional dependencies of set R1 can determine all the attributes which have been determined by the functional dependencies of set R2.
集合R1的功能依赖性可以确定所有由集合R2的功能依赖性确定的属性。
Thus, we conclude R1 is a subset of R2 i.e. R1 ⊃ R2.
因此，我们得出结论：R1是R2的子集，即R1⊃R2。

Case 3) Determining Whether Both R1 and R2 satisfy each other or not

情况3)确定R1和R2是否彼此满足

From Step 1, we conclude R2 ⊃ R1.
从步骤1，我们得出R2 2 R1。
From Step 2, we conclude R1 ⊃ R2.
从步骤2，我们得出R1 1 R2。
Thus, we conclude that both R1 and R2 satisfied each other i.e. R1 = R2.
因此，我们得出结论，R1和R2都彼此满足，即R1 = R2。