Decision-to-decision path

A decision-to-decision path, or DD-path, is a path of execution (usually through a flow graph representing a program, such as a flow chart) between two decisions. More recent versions of the concept also include the decisions themselves in their own DD-paths.

A flow graph of a program. Each color denotes a different DD-path. Nodes 1,2,5 and 6 are each in their own DD-path containing a single node. Nodes 3 and 4 together form one DD-path (they are a maximal chain).

Definition

In Huang's 1975 paper,[1] a decision-to-decision path is defined as path in a program's flowchart such that all the following hold (quoting from the paper):

  • its first constituent edge emanates either from an entry node or a decision box;
  • its last constituent edge terminates either at a decision box or at an exit node; and
  • there are no decision boxes on the path except those at both ends

Jorgensen's more recent textbooks restate it in terms of a program's flow graph (called a "program graph" in that textbook).[2] First define some preliminary notions: chain and a maximal chain. A chain is defined as a path in which:

  • initial and terminal nodes are distinct, and
  • all interior nodes have in-degree = 1 and out-degree = 1.

A maximal chain is a chain that is not part of a bigger chain.

A DD-path is a set of nodes in a program graph such that one of the following holds (quoting and keeping Jorgensen's numbering, with comments added in parentheses):[2]

  1. It consists of a single node with in-degree = 0 (initial node)
  2. It consists of a single node with out-degree = 0 (terminal node)
  3. It consists of a single node with in-degree ≥ 2 or out-degree ≥ 2 (decision/merge points)
  4. It consists of a single node with in-degree = 1 and out-degree = 1
  5. It is a maximal chain of length ≥ 1.

According to Jorgensen (2013), in Great Britain and ISTQB literature, the same notion is called linear code sequence and jump (LCSAJ).[2]

Properties

From the latter definition (of Jorgensen) we can conclude the following:

  • Every node on a flow graph of a program belongs to one DD-path.
  • If the first node on a DD-path is traversed, then all other nodes on that path will also be traversed.
  • The DD path graph is used to find independent path for testing.
  • Every statement in the program has been executed at least once.

DD-path testing

According to Jorgensen's 2013 textbook, DD-path testing is the best known code-based testing method, incorporated in numerous commercial tools.[2]

DD-path testing is also called C2 testing or branch coverage.[3][4]

See also

References
  1. Huang, J.C. (September 1975). "An Approach to Program Testing". Computing Surveys. 7 (3): 118–119. doi:10.1145/356651.356652. The definition given there is citing: "Fortran automated verification system Level 1 — user's guide, Program Validation Project, General Research Corp., October 1974."
  2. Paul C. Jorgensen (2013). Software Testing: A Craftsman’s Approach, Fourth Edition. CRC Press. pp. 136–137. ISBN 978-1-4665-6068-0.
  3. Judith A. Clapp; Saul F. Stanten; W.W. Peng; D.R. Wallace; Deborah A. Cerino; Roger J. Dziegiel Jr. (1995). Software Quality Control, Error, Analysis. William Andrew. pp. 347–348. ISBN 978-1-4377-4484-2.
  4. J. C. Huang (2009). Software Error Detection through Testing and Analysis. John Wiley & Sons. pp. 164–165. ISBN 978-0-470-46405-2.


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