Definition:

The dependence equation

• A dependence occurs between two statements S_p and S_q (not necessarily distinct), when there exists a pair of loop iterations I₁ and I₂, such that a memory reference in S_p^I₁ may refer to the same location as memory reference in S_q^I₂.

• This might occur if S_p and S_q refer to some common array A

• Suppose S_p refers to A[$\phi_p(I)$]
• Suppose S_q refers to A[$\phi_q(I)$]

• A dependence of some kind occurs between S_p and S_q if there exists a solution to the equation
  
  $$\phi_p(I_1) = \phi_q(I_2)$$
  
  
  for integer values of I₁ and I₂ lying within the loop bounds