BASIS PATH TESTING Path Testing Program graph is

BASIS PATH TESTING

Path Testing • Program graph is a directed graph in which – nodes are either entire statements or fragments of a statement, – edges represent flow of control. • The importance of the program graph is that program executions correspond to paths from the source to the sink nodes.

DD-Paths • The best known form of structural testing is based on a construct known as a decision-to-decision path (DD-Path) [Miller 77]. • The name refers to a sequence of statements that, in Miller’s words, begins with the “outway” of a decision statement and ends with the “inway” of the next decision statement. • There are no internal branches in such a sequence, so the corresponding code is like a row of dominoes lined up so that when the first falls, all the rest in the sequence fall. • DD-Paths in terms of paths of nodes in a directed graph. • We might call these paths chains, where a chain is a path in which the initial and terminal nodes are distinct, and every interior node has indegree = 1 and outdegree = 1.

• A DD-Path is a chain in a program graph such that – Case 1: it consists of a single node with indeg = 0, – Case 2: it consists of a single node with outdeg = 0, – Case 3: it consists of a single node with indeg ≥ 2 or outdeg ≥ 2, – Case 4: it consists of a single node with indeg = 1 and outdeg = 1, – Case 5: it is a maximal chain of length ≥ 1. • DD-Path graph is the directed graph in which – nodes are DD-Paths of its program graph, and – edges represent control flow between successor DD-Paths.

• Cases 1 and 2 establish the unique source and sink nodes of the program graph of a structured program as initial and final DD-Paths. • Case 3 deals with complex nodes; it assures that no node is contained in more than one DD-Path. • Case 4 is needed for “short branches”; it also preserves the one fragment, one DD-Path principle. • Case 5 is the “normal case”, in which a DD-Path is a single entry, single exit sequence of nodes (a chain). – The “maximal” part of the case 5 definition is used to determine the final node of a normal (non-trivial) chain.

Program Graph of the Triangle Program DD-Path Graph for the Triangle Program

Basis Path Testing • Notion of a “basis” has attractive possibilities for structural testing. • A basis in terms of a structure called a “vector space”, which is a set of elements (called vectors) and which has operations that correspond to multiplication and addition defined for the vectors. • Basis path testing is a white-box testing technique first proposed by Tom Mc. Cabe [MCC 76]. • The basis path method enables the test case designer to derive a logical complexity measure of a procedural design and use this measure as a guide for defining a basis set of execution paths. • Test cases derived to exercise the basis set are guaranteed to execute every statement in the program at least one time during testing.

• Cyclomatic complexity is a software metric that provides a quantitative measure of the logical complexity of a program. • CC defines the number of independent paths in the basis set of a program and • Provides us with an upper bound for the number of tests that must be conducted to ensure that all statements have been executed at least once. • An independent path is any path through the program that introduces at least one new set of processing statements or a new condition.

Complexity is computed in one of three ways: 1. The number of regions of the flow graph correspond to the cyclomatic complexity. 2. Cyclomatic complexity, V(G), for a flow graph, G, is defined as V(G) = E - N + 2 where E is the number of flow graph edges, N is the number of flow graph nodes. 3. Cyclomatic complexity, V(G), for a flow graph, G, is also defined as V(G) = P + 1 where P is the number of predicate nodes contained in the flow graph G.

1. The flow graph has four regions. 2. V(G) = 11 edges - 9 nodes + 2 = 4. 3. V(G) = 3 predicate nodes + 1 = 4.

• The following are basis paths for Triangle pbm. DD-Path Graph for the Triangle Program

• The problem here is that there are several inherent dependencies in the triangle problem. – One is that if three integers constitute sides of a triangle, they must be one of the three possibilities: equilateral, isosceles, or scalene. – A second dependency is that the three possibilities are mutually exclusive: if one is true, the other two must be false.

• We can identify several rules for the pbm: – If node B is traversed, then we must traverse nodes D and E. – If node C is traversed, then we must traverse nodes D and L. – If node E is traversed, then we must traverse one of nodes F, H, and J. – If node F is traversed, then we cannot traverse nodes H and J. – If node H is traversed, then we cannot traverse nodes F and J. – If node J is traversed, then we cannot traverse nodes F and I.

• The following feasible basis path set: • The triangle problem is atypical in that there are no loops. • The program has only 18 topologically possible paths, and of these, only the four basis paths listed above are feasible.