Definition-clear path

Concepts

A definition-clear path is a path which no other variable definition is made. <bib>vincenzi-etal:2007</bib>

Let x be a variable occurring in a program. A path <math>c = (i, n_1, . . . , n_m, j)</math>, <math>m >= 0</math> containing no definition of x in nodes <math>n_1, ..., n_m</math> is called a definition-clear path with respect to x from node <math>i</math> to node <math>j</math> and from node <math>i</math> to the edge <math>(n_m, j)</math>. <bib>vincenzi-etal:2007</bib>

A definition-clear path with respect to a variable x is a path between two nodes A and B, being x defined in A, with an use in B and there is no other definition of x in the other nodes present in the path between A and B. <bib>vincenzi-maldonado:slides:2007</bib>

Let a variable x defined at node i, and a use of x at node j. Consider the path <math>p = (i, n_{1}, n_{2}, ..., n_{k}, j), k >= 0</math>, that starts at node i, ends at node j, and nodes i and j do not occur along the subpath <math>n_{1}, n_{2}, ..., n_{k}</math>. The path p is a definition-clear path for variable x defined at node i and used at node j if x is not defined along the subpath <math>n_{1}, n_{2}, ..., n_{k}</math>. <bib>mathur:2008, 460</bib>