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sav08:review_of_fixpoints_in_semantics [2008/04/30 10:47] vkuncak |
sav08:review_of_fixpoints_in_semantics [2008/05/07 22:58] giuliano |
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| Program points are CFG nodes. Statements are labels on CFG edges. | Program points are CFG nodes. Statements are labels on CFG edges. | ||
| - | We look at a particular way of representing and computing sets of reachable, splitting states by program counter (control-flow graph node): **collecting semantics**. | + | We look at a particular way of representing and computing sets of reachable states, splitting states by program counter (control-flow graph node): **collecting semantics**. |
| $PS$ - the set of values of program variables (not including program counter). | $PS$ - the set of values of program variables (not including program counter). | ||
| Line 70: | Line 70: | ||
| Let $p_0$ be initial program counter and $I$ the set of values of program variables in $p_0$. | Let $p_0$ be initial program counter and $I$ the set of values of program variables in $p_0$. | ||
| - | The set of reachable states is defined as the least solution of: | + | The set of reachable states is defined as the least solution of constraints: |
| + | \[ | ||
| + | I \subseteq C(p_0) | ||
| + | \] | ||
| + | \[ | ||
| + | \bigwedge_{(p_1,p_2) \in E} sp(C(p),r(c(p_1,p_2)))) \subseteq C(p_2) | ||
| + | \] | ||
| + | where $c(p_1,p_2)$ is command associated with edge $(p_1,p_2)$, and $r(c(p_1,p_2))$ is the relation giving semantics for this command. | ||