# 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.

## 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][dubiousdiscuss]

## 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]