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.

DD-Path Graph for the Triangle Program

Program Graph of 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

McCabe [MCC76].

• 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.