Decision Table Testing)

Functional Testing: A program can be considered as a function that has inputs as a domain and outputs as a range.

　　　功能测试: 一个程序可以被看作是一个函数，它的输入是一个域，输出是一个范围。

Boundary Value Testing 边界值测试

1. Boundary Value Analysis 边界值分析
2. Robustness Testing 稳健性测试
3. Worst-Case Testing　　最坏情况下的测试
4. *Special Value Testing 特殊值测试
5. *Random Testing 随机测试

Boundary Value Analysis
The input variable values are used at their min, min+, nom, max-,max 输入变量的值在其最小值、最小+、正常值、最大-、最大时使用。
Text case generation: 文本案例的生成：
　　For all i 对于所有i
　　Values of all but one variable 𝑥_𝑖 at nominal 除一个变量外，其他所有变量的值均为名义值
　　𝑥_𝑖 assumes all 5 values from above 𝑥_𝑖 假设上述所有5个值
n variables yield 4n+1 test cases n个变量产生4n+1个测试案例

Robustness Testing

n variables yield 6n+1 test cases n个变量产生6n+1个测试案例

Worst-Case Testing

Robust Worst-Case Testing

Special Value Testing

Tester uses his domain knowledge, experience with same programs 测试者使用他的领域知识、相同程序的经验
No guidelines other than engineer’s judgment 除了工程师的判断外，没有其他准则
Also called “ad-hoc” or “seat-of-the pants” testing 也被称为 "临时性 "或 "裤裆 "测试
Despite all the apparent negatives, it can be useful 尽管有很多明显的负面因素，但它是有用的

Random Testing

The most widely practiced way of functional testing 最广泛采用的功能测试方式
Basic idea: 基本思想

Use a random number generator to produce random values (instead of max, min, … ) for test cases 使用随机数发生器为测试用例产生随机值（而不是最大、最小...）
Test cases are generated randomly until at least one of each output occurs 测试用例随机生成，直到每个输出中至少有一个出现。

Equivalence class testing

- A testing technique in which test data is derived by partitioning the input domain into disjoint sub-sets (equivalence classes).

一种测试技术，其中测试数据是通过将输入域划分为互不相干的子集（等价类）而得到的。

- Each of these classes is an equivalence partition where the program behaves in an equivalent way for each class member

这些类中的每一个都是一个等价分区，程序对每个类成员的行为都是等价的。

- where all members of a class are related (by an equivalence relation) 一个类的所有成员都有关系（通过等价关系）。
- Test cases are identified by using one element from each equivalence class. 测试用例通过使用每个等价类中的一个元素来确定。
- Underlying technique: Set partitioning 底层技术:集合分区。
Set Partitioning and Equivalence Relation
Given a set 𝐴, and a set of subsets 𝐴_1, A_2, …, A_n of 𝐴, the subsets are a partition of A iff:𝐴_1∪A_2∪…∪𝐴_𝑛=A and i≠𝑗⇒𝐴_𝑖∩A_j=∅

给定一个集合𝐴，以及𝐴的一组子集𝐴_1, A_2, ..., A_n，这些子集是A的一个分区，如果:𝐴_1∪A_2∪...∪𝐴_𝑛=A且i≠𝑗⇒𝐴_𝑖∩A_j=∅

A relation 𝑅⊆𝐴×𝐴 is an equivalence relation if R is reflexive, symmetric, and transitive. 一个关系𝑅⊆𝐴×𝐴是一个等价关系，如果R是自反的、对称的和传递的。
- Reflexive: ∀𝑎∈𝐴. (𝑎,𝑎)∈𝑅
- Symmetric: ∀𝑎, 𝑏∈𝐴. (𝑎,𝑏)∈𝑅⇒(𝑏, 𝑎)∈𝑅
- Transitive: ∀𝑎, 𝑏, 𝑐∈𝐴. (𝑎,𝑏)∈𝑅 ∧(𝑏, 𝑐)∈𝑅⇒(𝑎, 𝑐)∈𝑅

Each partition forms an equivalence class每个分区形成一个等价类

　　等价关系可以从输入、输出、计算等角度分析。

Equivalence Class Testing

Example:

Decision Table Testing

A testing technique in which test data is derived from a decision table. 一种测试技术，其中测试数据来自决策表。

Optimization
- Decision tables grow exponentially, if we add conditions. 如果我们增加条件，决策表会呈指数级增长。
- Number of columns = 2 ^(number of conditions) 列的数量=2^(个条件的数量)
- Optimizing size by 通过以下方式优化大小

Using “don’t care” values (*) May occur of a certain condition is irrelevant for an given action //使用 "不关心 "的值（*）:某个条件可能发生，但与给定的行动无关
Identifying impossible situations (-) May occur if conditions are not independent // 识别不可能的情况（-）:如果条件不独立，可能会发生

Example:
Exercise1

Exercise2

Rule count

- Limited entry tables with N conditions have 2^N rules 具有 N 个条件的有限入口表有 2N 个规则
- Don't care entries (*) and impossible situations (-) reduce the number of explicit rules by implying the existence of non-explicitly stated rules.

不要在乎条目（*）和不可能的情况（-）通过暗示存在非显式声明的规则来减少显式规则的数量。

- Counting rules of a given decision table: 给定决策表的计数规则：
- Rules with no (*) and (-) count as ‘1’ 没有（*）和（-）的规则计为“1”
- Roles with (*) and (-) count as 2i where i is the number of occurrences of (*) and (-) 带有（*）和（-）的角色计为 2i，其中 i 是（*）和（-）的出现次数
- Less rules than combination rule: count Indicates missing rules 规则少于组合规则计数:指示缺少规则
- More rules than combination rule count:Could indicate redundant rules, Could indicate inconsistent table 规则数多于组合规则计数:可能指示冗余规则,可能指示表不一致