Without SSA, you might have more definitions of that variable, and so not know it's exact value, type, etc, when you go to use it.
Without SSA form, to get that data you'd have to analyse the flow of the program (look at loops and if statements, etc).
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OK, english version: in program analysis, you want to know the value of a variable, so you create a "def-use chain" which connects a definition of a variable to all of its uses.
In some cases, you might have very many uses and definitions, esp of the same variable. In SSA form, each variable is only defined once, so you dont get pathological cases here.
The allows a flow-insensitive algorithm to approach the precision of a flow-sensitive algorithm.
English version: if you put something in SSA form, you can connect the use of a value directly to its definition (since it's only defined once, with one value).
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Does anyone have thoughts/opinions on the algorithm presented in "Simple and Efficient Construction of Static Single Assignment Form" by Braun, et al?