Control dependency

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Control dependency is a situation in which a program instruction executes if the previous instruction evaluates in a way that allows its execution.

An instruction B has a control dependency on a preceding instruction A if the outcome of A determines whether B should be executed or not. In the following example, the instruction ${\displaystyle S_{2}}$ has a control dependency on instruction ${\displaystyle S_{1}}$. However, ${\displaystyle S_{3}}$ does not depend on ${\displaystyle S_{1}}$ because ${\displaystyle S_{3}}$ is always executed irrespective of the outcome of ${\displaystyle S_{1}}$.

S1.         if (a == b)
S2.             a = a + b
S3.         b = a + b

Intuitively, there is control dependence between two statements A and B if

• B could be possibly executed after A
• The outcome of the execution of A will determine whether B will be executed or not.

A typical example is that there are control dependences between the condition part of an if statement and the statements in its true/false bodies.

A formal definition of control dependence can be presented as follows:

A statement ${\displaystyle S_{2}}$ is said to be control dependent on another statement ${\displaystyle S_{1}}$ iff

• there exists a path ${\displaystyle P}$ from ${\displaystyle S_{1}}$ to ${\displaystyle S_{2}}$ such that every statement ${\displaystyle S_{i}}$ ≠ ${\displaystyle S_{1}}$ within ${\displaystyle P}$ will be followed by ${\displaystyle S_{2}}$ in each possible path to the end of the program and
• ${\displaystyle S_{1}}$ will not necessarily be followed by ${\displaystyle S_{2}}$, i.e. there is an execution path from ${\displaystyle S_{1}}$ to the end of the program that does not go through ${\displaystyle S_{2}}$.

Expressed with the help of (post-)dominance the two conditions are equivalent to

• ${\displaystyle S_{2}}$ post-dominates all ${\displaystyle S_{i}}$
• ${\displaystyle S_{2}}$ does not post-dominate ${\displaystyle S_{1}}$