Function F with 2 Variables : x1 and x2 When F si implemented as a program, x1 and x2 will have some boundaries :

• a = <x1 =<b
• c = <x2 =<d

• BVA is Generalized in 2 ways :
  • by number of variables
    • a program is like a functio of n variables
    • one variable with min. min+, nom, max-, max, and the rest with nominal values
    • BVA yields 4n+1 test cases
  • by kinds of ranges
    • depend on the nature of variables
    • month--> can be encoded: Jan-1, Feb-2 (min-->Jan, min+-->Feb)
    • monthe cand be an enumerated type (for language supporting user-defined type)
    • a variable can be discrete bounded values
    • create bounded valued when no explicit bounds present
    • Boolean and Logical Variables present a problem for BVA

• BVA works well with several independent variables that represent bounded physical quantities
• some variables are dependent
  • month, year in NextDate^?
• BVA does not concern
  • nature of the function
  • semantic meaning of the variables

• is an extension of BVA
• includes min-, and max+ in BVA
• there is a problem for expected outputs
  • what happens when a physical quantity exceeds its maximumM
• Even strongly type implicit check for bounded values but we still need to perform explicit range checking and use exception handling to deal with robust values.

• Reject single fault assumption
  • what happens when one variable has an extreme values
• Worst-Case test cases come from cartesian product of five-element set
• BVA test cases are a proper subset of worst-case test cases
• yield 5n test cases
• Robust worst-case testing
  • involves the cartesian product of seven-element set

• or "ad-hoc testing"
• occurs when a tester
  • uses his/her domain knowledge
  • experience with similar programs
  • uses information about "soft spots" to devise test cases
• no guidance, just "best engineering judgement"
• depends on abilities of testers
• examples : test Feb 28, Feb 29, and Leap Years for NextDate^?

• Look at BVA of output range
• find input variable combinations that stress the boundary values $100, $1000, $1800, and $7,800

• rather than choosing min, min-, nom, max-, max, use a random number generator to pick test case values
• how many random test cases are sufficient?
  • Test cases are generated until at least one of each output occurs

• Test Methods base on input domain of a program
• input variables are independent
• unsatisfactory test cases can be generated (Feb 31, 1912)
• 2 distinctions :
  • normal VS robust values
  • single fault VS multiple fault assumption
• each testing method mentioned can be applied to output range
• domain analysis can be used for internal variables (loop counter, index, pointers)

• avoid redundancy
• form a partition of a set, where partition refers to a collection of mutually disjoint subsets (the union is the entire set)
• 2 implications of testing :
  • the entire set provide completeness
  • disjointendess ensures a form of redundancy
• equivalence class testing :
  • use one element from each equivalence class

• Use one variable from each equivalence class (interval) in a test case
• is based on single fault assumption

• is based on multipel fault assumption
• test each element of the Cartesian product of the equivalence classes
• the Cartesian product guarantees :
  • cover all equivanlence classes
  • cover each possible combination of inputs

• Robust - consider invalid values
• Weak - single fault assumption
• For valid inputs
  • use one value from each valid class
• For invalid inputs
  • ue one invalid value and the remaining values will be all valid
• Problem - specification does not define what the expected result should be for the invalid values

• Robust - consider invalid values
• Strong - multiple fault assumption
• Test cases are from each element of the Cartesian product of all the equivalence classes

• Use output equivalence class
• 4 possible outputs : Equilateral, Isosceles, Scalene, and Not ATriangle
• 4 output equivalence class :
  • R1 ={<a,b,c> : the triangle with sides a, b, and c is equilateral}
  • R2 ={<a,b,c> : the triangle with sides a, b, and c is isosceles}
  • R3 ={<a,b,c> : the triangle with sides a, b, and c is scalene}
  • R4 ={<a,b,c> : the triangle with sides a, b, and c do not form a triangle}