From b6c07f6d2825834538c2dd3d77e557ca74e15c9d Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 22 Oct 2025 16:22:26 +0200 Subject: [PATCH] [TI] Start multi band TM --- .../ti/parts/03_turing_machines/00_intro.tex | 2 +- .../01_multi-band-church-thesis.tex | 9 +++++++++ semester3/ti/ti-summary.pdf | Bin 937327 -> 460113 bytes semester3/ti/ti-summary.tex | 1 + 4 files changed, 11 insertions(+), 1 deletion(-) create mode 100644 semester3/ti/parts/03_turing_machines/01_multi-band-church-thesis.tex diff --git a/semester3/ti/parts/03_turing_machines/00_intro.tex b/semester3/ti/parts/03_turing_machines/00_intro.tex index 703353d..48cf517 100644 --- a/semester3/ti/parts/03_turing_machines/00_intro.tex +++ b/semester3/ti/parts/03_turing_machines/00_intro.tex @@ -44,7 +44,7 @@ Mit einem TM die Sprache $\{ 0^n 1^n \divides n \in \N \}$ erkennen kann man nun beispielsweise, wenn das Eingabealphabet $\Sigma = \{ 0, 1 \}$, dann könnte man $\Gamma$ das Symbol $2$ hinzufügen, mit dem man jedes bearbeitete Symbol ersetzt. Im Buch wird als Beispiel auf Seite 99ff (= Seite 114ff im PDF) ein komplexeres Wort gewählt, -bei welchem ein zeichen $a \in \alphabetbool$ durch $(a, B) \in \alphabetbool \times \{ A, B \}$ ersetzt wird, +bei welchem ein Zeichen $a \in \alphabetbool$ durch $(a, B) \in \alphabetbool \times \{ A, B \}$ ersetzt wird, da wir zwei Phasen haben und zwischen denen unterscheiden wollen können. % 113 diff --git a/semester3/ti/parts/03_turing_machines/01_multi-band-church-thesis.tex b/semester3/ti/parts/03_turing_machines/01_multi-band-church-thesis.tex new file mode 100644 index 0000000..4b6858c --- /dev/null +++ b/semester3/ti/parts/03_turing_machines/01_multi-band-church-thesis.tex @@ -0,0 +1,9 @@ +\newsection +\subsection{Mehrband-Turingmaschinen und Church'sche These} +Die Turingmaschinen sind das Standardmodell der Berechenbarkeitstheorie, aber benötigen einige Modifikationen, um wirklich geeignet zu sein +(da das Von-Neumann Modell physisch unterschiedliche CPU, Eingabemedium und Speicher für Programme und Daten fordert, aber die TM ein gemeinsames Eingabemedium und Speicher hat). + +Eine $k$-Ban-Turingmaschine (für $k \in \N_0$) hat folgende Komponenten: +\begin{itemize} + \item +\end{itemize} diff --git a/semester3/ti/ti-summary.pdf b/semester3/ti/ti-summary.pdf index 5f1d969c43bb99265821803674fa091197b6f456..acb1ff4079b2234893ddcb920425ac721b379b8a 100644 GIT binary patch delta 7873 zcmZvBRZyKlw=C}N4k5S&hYbWmaA)K0?oP0LxH}sOn&9s4?oNURcXzj&|6HrO=T=Sk z%c_}&UR7OdR-dPXW+KU|rIGPLRP0oaCN?NSLMWf)%^fV=tf)9RQoHdmn1BKeIoB0Q zw9aGAlN)h`iCf_oz4hh(OXi4G?4lnL8L+HiI@Sa`8KxgQvt0%(H4sK^*||eeoM8Cs zZ@yao2~xeo13L?5E>DvE{VJpp;WTo&EHPT*(dxfR6cXWEFcXE!GRm2kAJzIrvlYY` z)t%H?j|=77On6=)dbsfEWI*&C$%3_dy`nrqYQ|XxZdxXNQWu?KAoiOtdXZ40nStV& z2uH1doo#P%J;&p$TnZI2m_X*|f*J3leQ*2m(D&zf2=!MmF6o)cRyvp!#KDq#;e`#^ zA%e{Khz5L6;4jj!ogv*yfx(xRFs&mk32#iu?&Pp3hYw{mT_F%A8i&Nek06HsMS$1Q#|Dy!MW$d zdkuWh6RWt<*3b8or_wCEZof9;m`c#eXT`Bk;gfdnxWt3;0`iAjNb*Ikluj9+6Y-Dd 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a/semester3/ti/ti-summary.tex b/semester3/ti/ti-summary.tex index 1a34b57..48a82eb 100644 --- a/semester3/ti/ti-summary.tex +++ b/semester3/ti/ti-summary.tex @@ -88,6 +88,7 @@ \section{Turing-Maschinen} \setcounter{subsection}{2} \input{parts/03_turing_machines/00_intro.tex} +\input{parts/03_turing_machines/01_multi-band-church-thesis.tex} \end{document}