Editing Use-define chain (section)

==Execution==

Consider the sequential execution of the list of statements, {{tmath|s(i)}}, and what can now be observed as the computation at statement, ''j'':

*A definition at statement {{tmath|s(i)}} with ''i'' &lt; ''j'' is '''alive''' at ''j'', if it has a use at a statement {{tmath|s(k)}} with ''k'' ≥ ''j''. The set of alive definitions at statement ''i'' is denoted as {{tmath|A(i)}} and the number of alive definitions as <math>|A(i)|</math>.  ({{tmath|A(i)}} is a simple but powerful concept: theoretical and practical results in [[space complexity theory]], [[access complexity]](I/O complexity), [[register allocation]] and [[memory locality|cache locality]] exploitation are based on {{tmath|A(i)}}.)
*A definition at statement {{tmath|s(i)}} '''kills''' all previous definitions ({{tmath|s(k)}} with ''k'' &lt; ''i'') for the same variables.