diff --git a/semester3/ti-compact/parts/04_computability.tex b/semester3/ti-compact/parts/04_computability.tex index 8c23fa2..1bfd353 100644 --- a/semester3/ti-compact/parts/04_computability.tex +++ b/semester3/ti-compact/parts/04_computability.tex @@ -159,6 +159,13 @@ or the condition can be restated such that only $L(M)$ is described by it. For a more formal proof of that condition, simply show that the implication holds +Another result (not formally proven in the script, but there is a proof by intimidation) that can come in useful, especially when trying to show $L \notin \cL_{RE}$ is: +\rmvspace +\begin{align*} + L, L^C \in \cL_{RE} \Longleftrightarrow L \in \cL_R +\end{align*} + + \stepcounter{subsection} \subsection{The method of the Kolmogorov-Complexity} \inlinetheorem The problem of computing the Kolmogorov-Complexity $K(x)$ for each $x$ is algorithmically unsolvable. diff --git a/semester3/ti-compact/ti-compact.pdf b/semester3/ti-compact/ti-compact.pdf index c832fa4..623c2c5 100644 Binary files a/semester3/ti-compact/ti-compact.pdf and b/semester3/ti-compact/ti-compact.pdf differ