From d3a1df6a06ea347edbb8b2faf6e466de6b5a5967 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 10 Dec 2025 10:18:00 +0100 Subject: [PATCH] [TI] Compact: Add another result --- .../ti-compact/parts/04_computability.tex | 7 +++++++ semester3/ti-compact/ti-compact.pdf | Bin 380186 -> 380396 bytes 2 files changed, 7 insertions(+) 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 c832fa49cf5caabc06c730c883cb57983f7fbecb..623c2c58c5bd2e78e04802e871b12bf023ae8b7b 100644 GIT binary patch delta 33919 zcmV)MK)An}niuSw7qDFk0W^~l0x5r`RZDNwFc7}yS6G}Jsqy+1JLU$ZZ)l5lB_s-m zG|e{YZW735LG6XV&Nz1V(e5G;ha?kwo}XtvQ*@6gItkuRg3&QgkRe8Kg(g!Z4N+7f zZ6q-|Mw2^qgC|Aaw0T!%={$^t5csgEzAd}FwSN+ivof!<+-*f}&1$4s7e;?v8O88< 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