2 White-box testing

• Also called structural or code-based testing.
• Designs test cases based on the program’s internal structure (the “how”), not just its specification.
• Foundation: Control-Flow Graph (CFG) – a graph where nodes are statements/basic blocks and edges represent control flow.

2. Basic Coverage Criteria

Coverage measures what code is executed by a test suite. Criteria form a hierarchy: Statement ⊂ Branch ⊂ Condition.

Criterion	Goal	Key Point
Statement Coverage	Execute every statement at least once.	One test may suffice for straight-line code.
Branch Coverage	Execute every true/false branch of each decision.	Requires ~2 tests per if. Stronger than statement coverage.
Condition Coverage	Each atomic Boolean condition (e.g., x>0) evaluates to true and false at least once.	With short-circuit evaluation, it can be stronger than branch coverage.

3. Illustrative Example

int example(int x, int y) {
    int z = 0;               // Stmt 1
    if (x > 0 && y > 0) {    // Decision with two conditions
        z = x;               // Stmt 2
    }
    return z;                // Stmt 3
}

Coverage demonstration:

• Statement: example(1,1) executes all 3 statements.
• Branch: Need example(1,1) (true branch) and example(0,1) (false branch).
• Condition: Need tests for:
  • x>0=F, y>0=T → example(0,1) (short-circuits)
  • x>0=T, y>0=T → example(1,1) (Not required if we dont have short circuit)
  • x>0=T, y>0=F → example(1,0).

1. Advanced Coverage Criteria

• MC/DC (Modified Condition/Decision Coverage): Required for safety-critical software (e.g., DO-178C).
  • Needs statement, branch, and condition coverage.
  • Plus: Each condition must independently affect the decision’s outcome.
  • Example: For a AND (b OR c), 4 tests suffice (vs. 8 for full condition combination).
• Path Coverage: Execute all CFG paths. Generally impossible with loops – motivates approximations.
• Basis-Path Coverage: Cover a finite set of linearly independent paths. Number of basis paths = cyclomatic complexity.

2. Cyclomatic Complexity

• Formula: $V(G)=E-N+2$ (where $E$=edges, $N$=nodes in CFG).
• Interpretation: Measures the number of basis paths; a higher value indicates more complex control flow.

3. Data-Flow Testing Concepts (Brief)

• DEF(v, n): Node n defines (writes) variable v.
• USE(v, n): Node n uses (reads) v.
• DU-path: A path from a DEF to a USE of the same variable.
• DC-path: A DU-path with no intervening DEF of that variable.
• Slicing: Isolating program parts relevant to a specific variable at a point. E.g., a backward slice finds all nodes contributing to a variable’s value.

6. Comparison of Criteria

Criterion	Typical # Tests	Strength	Practical Use
Statement	Minimal	Weak	Baseline
Branch	~2× statement	Moderate	Industry standard
Condition	$2^n$ (n conditions)	Strong	Thorough
MC/DC	$n+1$ (n conditions)	Very Strong	Safety-critical systems
Path	Infinite (with loops)	Strongest	Theoretical ideal