Foundations: start subsection on basic block definition

manuscrit/20_foundations/20_code_analyzers.tex

@@ -427,3 +427,44 @@ for large values of $n$ in this manuscript whenever it is clear that this value
 is a measure.
 
 \subsubsection{Basic block of an assembly-level program}
+
+Code analyzers are meant to analyze sections of straight-line code, that is,
+portions of code which do not contain control flow. As such, it is convenient
+to split the program into \emph{basic blocks}, that is, portions of
+straight-line code linked to other basic blocks to reflect control flow. We
+define this notion here formally, to use it soundly in the following chapters
+of this manuscript.
+
+\begin{notation}
+    For the purposes of this section,
+    \begin{itemize}
+        \item we formalize a segment of assembly code as a sequence of
+            instructions;
+        \item we confuse an instruction with its address.
+    \end{itemize}
+
+    \smallskip{}
+
+    An instruction is said to be a \emph{flow-altering instruction} if this
+    address may alter the normal control flow of the program. This is typically
+    true of jumps (conditional or unconditional), function calls, function
+    returns, \ldots
+
+    \smallskip{}
+
+    An address is said to be a \emph{jump site} if any flow-altering
+    instruction in the considered sequence may alter control to this address
+    (and this address is not the natural flow of the program, \eg{} in the case
+    of a conditional jump).
+\end{notation}
+
+\begin{definition}[Basic block decomposition]
+    \todo{}
+\end{definition}
+
+\begin{remark}
+    This definition gives a direct algorithm to split a segment of assembly
+    code into basic blocks, as long as we have access to a semantics of the
+    considered assembly that indicates whether an instruction is flow-altering,
+    and if so, what are its possible jump sites.
+\end{remark}