diff --git a/manuscrit/20_foundations/20_code_analyzers.tex b/manuscrit/20_foundations/20_code_analyzers.tex index 03d34a8..2a7de56 100644 --- a/manuscrit/20_foundations/20_code_analyzers.tex +++ b/manuscrit/20_foundations/20_code_analyzers.tex @@ -394,7 +394,7 @@ referred to as its \emph{IPC} (its unit). For an integer number of kernel iterations $n$, $\sfrac{\Delta_n\text{ret}}{\card{\kerK}} = n$. While measurement errors may make $\Delta_{n}\text{ret}$ fluctuate slightly, this - fluctuation will be below a constant threshold: + fluctuation will be below a constant threshold. \[ \abs{\dfrac{\Delta_n\text{ret}}{\card{\kerK}} - n} \leq E_\text{ret} @@ -407,8 +407,20 @@ referred to as its \emph{IPC} (its unit). \] with $E_C$ a constant. - As such, for a given $n$, \todo{} -\end{proof} + As those errors are constant, while other quantities are linear, we thus + have + + \[ + \cycmes{\kerK}{n} = \dfrac{\Delta_n C}{\sfrac{\Delta_n + ret}{\card{\kerK}}} \limarrow{n}{\infty} \dfrac{C(\kerK^n)}{n} + \] + + and, composing limits with the previous lemma, we thus obtain + + \[ + \cycmes{\kerK}{n} \limarrow{n}{\infty} \cyc{\kerK} + \] + \end{proof} Given this property, we will use $\cyc{\kerK}$ to refer to $\cycmes{\kerK}{n}$ for large values of $n$ in this manuscript whenever it is clear that this value