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--- sav08:collecting_semantics [2008/05/07 08:10]
vkuncak
+++ sav08:collecting_semantics [2015/04/21 17:30] (current)
@@ Line 9: / Line 9: @@
 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).
@@ Line 20: / Line 20: @@
 The set of reachable states is defined as the least solution of constraints:
-\[
+\begin{equation*}
   I \subseteq C(p_0)
-\]
+\end{equation*}
-\[
+\begin{equation*}
   \bigwedge_{(p_1,p_2) \in E} sp(C(p_1),r(p_1,p_2))) \subseteq C(p_2)
-\]
+\end{equation*}
 over variables $C(p)$ for all of finitely many program points $p$.
+The last condition is equivalent to
+\begin{equation*}
+  \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)
+\end{equation*}
 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>
+After the assignment of $x$ to 2, the set of reachable states $C$ is $C = \{ (x,2), (i,20), (y,t) \}$