软件测试和软件质量-朱蔚恒-2.ppt

软件测试与软件质量 朱蔚恒 09.春 珠海学院 Overview 测试人员的离散数学 集合论 函数 关系 概率 图 Representation Paths Directed Graphs Graphs for Testing 集合定义 列举: Example: Y = {10, 20, 30, 40} 使用判断规则: Examples: Y = {item_number | 80 item_number 100} Y = {x | x is positive integer} Y = {x | PI(x)} 空集: Y = {year : 2012 year 1812} = {} = O 文氏图 Diagrams that illustrate different set relationships or illustrate a set with respect to the domain (U) 集合运算: 并Union : A U B = { x : x in A or x in B} 交Intersection: A ∩ B = {x : x in A and x in B} 补Complement: A* = {x : x not in A} 相对补Relative complement: A – B = {x : x in A and x not in B} 对称差Symmetric difference: A B = {x: x in A x in B} = (A U B) – (A ∩ B) 集合关系和划分 子集A Subset B: a in A ? a in B 真子集A Proper Subset B: A subset B and (B – A) ≠ O 两集合相等Equal sets: A = B iff A subset B and B subset A 划分Given a set B and a set of subsets A1, A2, An of B, the subsets are a partition of B iff A1 U A2 U .. An = B For i ≠ j Ai ∩Aj = O 函数，定义域，值域 Given two sets A and B, a function f :A ? B is a subset of the product A X B such that for any of ai, aj in A, there exist bi, bj in B such that f(ai) = bi, and f(aj) = bj. The set A is called the domain of f and B is called the range of f. The function f can be represented as a set of pairs. 函数类型 Functions are further described by the particulars of the mapping e.g. f(A) = {bi in B : bi = f(ai) for some ai in A} This set is sometimes called the image of A under f Types of functions that relate the image and the range are: Function f is a function of A onto B iff f(A) = B Function f is a function of A into B iff f(A) proper subset B Function f is a one-to-one function from A to B iff for all ai, aj in A, s.t. ai ≠aj implies that f(ai) ≠ f(aj) 复合函数 Suppose we have sets and functions such that the range of one is the domain of the next: f: A ? B g: B ? C h: C ? D We can define a new function w:A ? D such that w(a) = (h o g o f) (a) = h(g(f(a))) So, if f(a) = b, and g(b) = c, and h(c) = d then w(a) = h