From fc3e3ea5f019b435b6853cdb1971bd94bb7bffc4 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Tue, 9 Dec 2025 09:06:51 +0100 Subject: [PATCH] [TI] Fixes --- .../ti-compact/parts/04_computability.tex | 9 ++++++++- semester3/ti-compact/parts/05_complexity.tex | 2 ++ semester3/ti-compact/ti-compact.pdf | Bin 378427 -> 378963 bytes 3 files changed, 10 insertions(+), 1 deletion(-) diff --git a/semester3/ti-compact/parts/04_computability.tex b/semester3/ti-compact/parts/04_computability.tex index 1512d14..d9191b7 100644 --- a/semester3/ti-compact/parts/04_computability.tex +++ b/semester3/ti-compact/parts/04_computability.tex @@ -154,4 +154,11 @@ 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 -As of HS2025, chapters 5.5 and 5.6 are not relevant for the Endterm or Session exam, so they are omitted here +\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. + +\inlinelemma If $L_H \in \cL_R$, then there exists an algorithm to compute the Kolmogorov-Complexity $K(x)$ for each $x \in \wordbool$ + + +As of HS2025, chapters 5.5 and 5.7 are not relevant for the Endterm or Session exam, so they are omitted here diff --git a/semester3/ti-compact/parts/05_complexity.tex b/semester3/ti-compact/parts/05_complexity.tex index f4b86c7..9430469 100644 --- a/semester3/ti-compact/parts/05_complexity.tex +++ b/semester3/ti-compact/parts/05_complexity.tex @@ -181,3 +181,5 @@ A few languages commonly used to show $NP$-completeness: \end{itemize} where a clique is \TODO Add. and a vertex cover is any set $U \subseteq V$ where all edges $\{ u, v \} \in E$ have at least one endpoint $u, v \in U$ + +We have $SAT \leq_p \text{CLIQUE}$, $SAT \leq 3SAT$, $\text{CLIQUE} \leq VC$ diff --git a/semester3/ti-compact/ti-compact.pdf b/semester3/ti-compact/ti-compact.pdf index e40bcc53e89438ed024b24cbf1b40e2f601f4f0c..26290b365d8e27a26c27aeab7875bbcae7cd79e6 100644 GIT binary patch delta 23410 zcmZs>bx>SU^Ck=fgS)#23-0djuEE`1f@E-lJA=Cf2@Zq1dxE>W28SSD-uL&_Zq@Go zbE~_b?sNLwTXnmu&(jf$KbMGKCx-~;AOT`E8X(rfq!jMrz;Li}q_{CNfD9Bp)_JhH zXKGC^toXHQm4y&D7o$=fbF>*%w3;Jn;GLy3R_VskWz47D?##Y>qsx#J?GETr| ziTUioyhvhaFs;hy-%XvyOf1~i)_;#~+Rl&#FJUrksi0(ct`rmWSYr7*QGPLE6)ZDFpArS%n%FgK3VnVa_Qh7nVo>wDP3yc#W8369lMQiz$7j87Zg!oWc|_az92KQ zXgp(&RZfS9)8#$0^%!7#%A+%`mBzfAsg_zNb>-WFvl<&UOZ) zI(AVDF+5zH1LdrLQCh*h530Fo6rp_kvn@6O;+9vs*01RPU2J-~!d7+jEUIaDoQI{D zI*PBRpHlTzn>6UWctF`|$6vDJj+4Hsa($cad(hTCzVe&0o$*@2@w+HmxR14{52IFK zSQe*DSHaokpSVfIMfnb0r0A+}_f!Z)dBA?3Y@yVp2P39IOYj`3B^@lx58$yG 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