Secciones/incremental_slicing.tex

@@ -10,7 +10,7 @@ The system dependence graph (SDG) is a method for program slicing that was first
 proposed by Horwitz, Reps and Blinkey \cite{HorwitzRB88}. It builds upon the
 existing control flow graph (CFG), defining dependencies between vertices of the
 CFG, and building a program dependence graph (PDG), which represents them. The
-system dependence graph (SDG) is then build from the assembly of the different
+system dependence graph (SDG) is then \added{built}\deleted{build} from the assembly of the different
 PDGs (each representing a method of the program), linking each method call to
 its corresponding definition. Because each graph is built from the previous one,
 new constructs can be added with to the CFG, without the need to alter the
@@ -35,12 +35,14 @@ predicate.
 
 \begin{definition}[Control Flow Graph~\cite{???}]
 	A \emph{control flow graph} $G$ of a program $P$ is a tuple $\langle N, E \rangle$, where $N$ is a set of nodes, composed of a method's statements and two special nodes, ``Start'' and ``End''. $E$ is a set of edges of the form $e = \left(n_1, n_2\right)$ a directed edge from $n_1$ to $n_2$
+	
+	\josep{solo has dicho la parte sintactica. Yo añadiría que existe un arco de el nodo $n_1$ al nodo $n_2$ si y solo si, en alguna ejecución, $n_2$ es ejecutado inmediatamente despues de $n_1$}
 \end{definition}
 
 To build the PDG and then the SDG, some dependencies must be extracted from the CFG, which are defined as follows:
 
 \begin{definition}[Postdominance]
-	Vertex $b$ \textit{postdominates} vertex $b$ if and only if $a \neq b$ and $b$ is on every path from $a$ to the ``End'' vertex.
+	Vertex $b$ \textit{postdominates} vertex \added{$a$}\deleted{$b$} if and only if $a \neq b$ and $b$ is on every path from $a$ to the ``End'' vertex.
 \end{definition}
 
 \begin{definition}[Control dependency]
@@ -48,8 +50,10 @@ To build the PDG and then the SDG, some dependencies must be extracted from the
 	Vertex $b$ is \textit{control dependent} on vertex $a$ ($a \ctrldep b$) if and only if $b$ postdominates one but not all of $a$'s successors. It follows that a vertex with only one successor cannot be the source of control dependence.
 \end{definition}
 
+\josep{de donde has sacado esta definicion? La veo incorrecta. Por ejemplo, si tenemos $if ~a ~then ~b$, $b$ no postdomina ningun sucesor de $a$}
+
 \begin{definition}[Data dependency]
-	Vertex $b$ is \textit{data dependent} on vertex $a$ ($a \datadep b$) if and only if $a$ may define a variable $x$, $b$ may use $x$ and there an $x$-definition free path from $a$ to $b$.\footnote{The initial definition of data dependency was further split into in-loop data dependencies and the rest, but the difference is not relevant for computing the slices in the SDG.}
+	Vertex $b$ is \textit{data dependent} on vertex $a$ ($a \datadep b$) if and only if $a$ may define a variable $x$, $b$ may use $x$ and there \added{exists} an $x$-definition free path from $a$ to $b$.\footnote{The initial definition of data dependency was further split into in-loop data dependencies and the rest, but the difference is not relevant for computing the slices in the SDG.}
 \end{definition}
 
 It should be noted that variable definitions and uses can be computed for each
@@ -59,7 +63,7 @@ left-hand side of assignments. Similarly, no instruction defines variables,
 except those in the left-hand side of assignments. The variables used and
 defined by a procedure call are those used and defined by its body.
 
-With the data and control dependencies, the PDG may be built, by replacing the
+With the data and control dependencies, the PDG may be built\deleted{,} by replacing the
 edges from the CFG by data and control dependence edges. The first tends to be
 represented as a thin solid line, and the latter as a thick solid line. In the
 examples, data dependencies will be thin solid red lines.