Secciones/incremental_slicing.tex

@@ -39,7 +39,7 @@ to the result of evaluating the conditional expression in the guard of the
 predicate.
 
 \begin{definition}[Control Flow Graph \carlos{add original citation}]
-	A \emph{control flow graph} $G$ of a program\sergio{program o method?} $P$ is a directed graph, represented as a tuple $\langle N, E \rangle$, where $N$ is a set of nodes, composed of a method's\sergio{method o program?} statements plus two special nodes, ``Start'' and ``End''; and $E$ is a set of edges of the form $e = \left(n_1, n_2\right) | n_1, n_2 \in N$. 
+	A \emph{control flow graph} $G$ of a program\sergio{program o method?} $P$ is a directed graph, represented as a tuple $\langle N, E \rangle$, where $N$ is a set of nodes \josep{such that for each statement $s$ in $P$there is a node in $N$ labeled with $S$ and there are two special nodes...}, composed of a method's\sergio{method o program?} statements plus two special nodes, ``Start'' and ``End''; and $E$ is a set of edges of the form $e = \left(n_1, n_2\right) | n_1, n_2 \in N$. 
 	\josep{Esto es una definicion. No pueden haber opinion ni contenido vago. O defines que Start y End son nodos o no lo defines. Pero no diugas lo que han hecho otros en una definicion. Lo que sigue yo lo quitaría}
 	Most algorithms\added{, in order} to generate the SDG\added{,} mandate the ``Start'' node to be the only source and \added{the} ``End'' \added{node} to be the only sink in the graph. \carlos{Is it necessary to define source and sink in the context of a graph?}\josep{quitalo}.
 
@@ -50,19 +50,22 @@ To build the PDG and then the SDG, there are two dependencies based directly on
 
 \begin{definition}[Postdominance \carlos{add original citation?}]
 	\label{def:postdominance}
-	Vertex $b$ \textit{postdominates} vertex $a$ if and only if $b$ is on every path from $a$ to the  ``End'' vertex.
+	\josep{Let $C = (N,E)$ be a CFG.}
+	Vertex $b\josep{\in N}$ \textit{postdominates} vertex $a\josep{\in N}$ if and only if $b$ is on every path from $a$ to the  ``End'' vertex.
 \end{definition}
 
 \begin{definition}[Control dependency\sergio{dependency o dependence?} \carlos{add original citation}]
 	\label{def:ctrl-dep}
-	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.
+	\josep{Let $C = (N,E)$ be a CFG.}
+	Vertex $b\josep{\in N}$ is \textit{control dependent} on vertex $a\josep{\in N}$ ($a \ctrldep b$) if and only if $b$ postdominates one but not all of $a$'s successors. \josep{Lo que sigue es en realidad es un lema. No hace falta ponerlo como lema, pero sí sacarlo a después de la definicion.}It follows that a vertex with only one successor cannot be the source of control dependence.
 \end{definition}
 
 \begin{definition}[Data dependency\sergio{dependency o dependence?} \carlos{add original citation}]
 	\label{def:data-dep}
-	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 exists a \carlos{could it be ``an''??} $x$-definition free path from $a$ to $b$.
+	\josep{Let $C = (N,E)$ be a CFG.}
+	Vertex $b\josep{\in N}$ is \textit{data dependent} on vertex $a\josep{\in N}$ ($a \datadep b$) if and only if $a$ may define a variable $x$, $b$ may use $x$ and there exists a \carlos{could it be ``an''??} $x$-definition free path from $a$ to $b$.
 	
-	Data dependency was originally defined as flow dependency, and split into loop and non--loop related dependencies, but that distinction is no longer useful to compute program slices \sergio{Quien dijo que ya no es util? Vale la pena citarlo?}.
+	Data dependency was originally defined as flow dependency, and split into loop and non--loop related dependencies\josep{creo que es loop-carried. Me parece que esta en el paper de Frank Tip}, but that distinction is no longer useful to compute program slices \sergio{Quien dijo que ya no es util? Vale la pena citarlo?}. \josep{Si que es useful en program slicing, pero no en debugging.}
 	It should be noted that variable definitions and uses can be computed for each statement independently, analysing the procedures called by it if necessary. The variables used and defined by a procedure call are those used and defined by its body.
 \end{definition}
 
@@ -73,9 +76,9 @@ examples, \added{data and control dependencies are represented by thin solid red
 
 \begin{definition}[Program dependence graph]
 	\label{def:pdg}
-	The \textsl{program dependence graph} (PDG) is a directed graph (and originally a tree\sergio{???}) represented by three elements: a set of nodes $N$, a set of control edges $E_c$ and a set of data edges $E_d$. \sergio{$PDG = \langle N, E_c, E_d \rangle$}
+	\josep{Given a program $P$,} The \textsl{program dependence graph} (PDG) \josep{associated with $P$} is a directed graph (and originally a tree\sergio{???}\josep{sobran las aclaraciones historicas en una definicion}) represented by \josep{a triple $\langle N, E_c, E_d \rangle$ where $N$ is...} three elements: a set of nodes $N$, a set of control edges $E_c$ and a set of data edges $E_d$. \sergio{$PDG = \langle N, E_c, E_d \rangle$}
 
-	The set of nodes corresponds to the set of nodes of the CFG, excluding the ``End'' node.
+	The set of nodes corresponds to the set of nodes of the CFG\josep{que CFG? no se puede dar por hecho que existe un CFG en una definicion}, excluding the ``End'' node.
 	
 	Both sets of edges are built as follows. There is a control edge between two nodes $n_1$ and $n_2$ if and only if $n_1 \ctrldep n_2$\sergio{acordarse de lo de evitar la generacion de arcos para prevenir la transitividad. Decidir si definimos Control arc como ua definicion aparte.}, and a data edge between $n_1$ and $n_2$ if and only if $n_1 \datadep n_2$. Additionally, if a node $n$ does not have any incoming control edges, it has a ``default'' control edge $e = (\textnormal{Start},n)$; so that ``Start'' is the only source node of the graph.