tobast/phd-thesis
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity

Foundations: finish \cyc definition/properties

Browse source
This commit is contained in:
Théophile Bastian 2024-01-31 18:09:46 +01:00
parent 39d8741ae7
commit f82ec7f5f6
1 changed files with 15 additions and 3 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

18
manuscrit/20_foundations/20_code_analyzers.tex
View file

@ -394,7 +394,7 @@ referred to as its \emph{IPC} (its unit).
For an integer number of kernel iterations $n$, For an integer number of kernel iterations $n$,
$\sfrac{\Delta_n\text{ret}}{\card{\kerK}} = n$. While measurement $\sfrac{\Delta_n\text{ret}}{\card{\kerK}} = n$. While measurement
errors may make $\Delta_{n}\text{ret}$ fluctuate slightly, this errors may make $\Delta_{n}\text{ret}$ fluctuate slightly, this
fluctuation will be below a constant threshold: fluctuation will be below a constant threshold.
\[ \[
\abs{\dfrac{\Delta_n\text{ret}}{\card{\kerK}} - n} \abs{\dfrac{\Delta_n\text{ret}}{\card{\kerK}} - n}
\leq E_\text{ret} \leq E_\text{ret}
@ -407,8 +407,20 @@ referred to as its \emph{IPC} (its unit).
\] \]
with $E_C$ a constant. with $E_C$ a constant.
As such, for a given $n$, \todo{} As those errors are constant, while other quantities are linear, we thus
\end{proof} 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 $\cycmes{\kerK}{n}$ 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 for large values of $n$ in this manuscript whenever it is clear that this value