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sav08:collecting_semantics [2008/05/07 08:10] vkuncak |
sav08:collecting_semantics [2008/05/08 12:37] vkuncak |
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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**. |
| $PS$ - states describing values of program variables (not including program counter). | $PS$ - states describing values of program variables (not including program counter). | ||
| Line 27: | Line 27: | ||
| \] | \] | ||
| over variables $C(p)$ for all of finitely many program points $p$. | over variables $C(p)$ for all of finitely many program points $p$. | ||
| + | |||
| + | The last condition is equivalent to | ||
| + | \[ | ||
| + | \bigwedge_{p_2 \in V}\ \left( C(p_2) = C(p_2) \cup \bigcup_{(p_1,p_2) \in E} sp(C(p_1),r(p_1,p_2))) \right) | ||
| + | \] | ||
| Here $r(p_1,p_2)$ is the relation giving semantics for the command associated with edge $(p_1,p_2)$. | Here $r(p_1,p_2)$ is the relation giving semantics for the command associated with edge $(p_1,p_2)$. | ||
| Line 53: | Line 58: | ||
| } | } | ||
| </code> | </code> | ||
| + | After the assignment of $x$ to 2, the set of reachable states $C$ is $C = \{ (x,2), (i,20), (y,t) \}$ | ||