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[TI] Compact: Add better explanation

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Janis Hutz
2025-11-04 15:57:36 +01:00
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semester3/ti-compact/parts/03_turing-machines.tex
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@@ -26,14 +26,14 @@ As with normal TMs, the Turing Machine $M$ accepts $w$ if and only if $M$ reache
Church's Thesis states that the Turing Machines are a formalization of the term ``Algorithm''.
It is the only axiom specific to Computer Science.
All the words that can be accepted by a Turing Machine are elements of $\mathcal{L}_{RE}$ and are called \bi{recursively enumerable}.
All the words that can be accepted by a Turing Machine are elements of $\cL_{RE}$ and are called \bi{recursively enumerable}.
\subsection{Non-Deterministic Turing Machines}
The same ideas as with NFA apply here. The transition function also maps into the power set:
\rmvspace
\begin{align*}
\delta : (Q - \{ \qacc, \qrej \}) \times \Gamma \rightarrow \mathcal{P}(Q \times \Gamma \times \{ L, R, N \})
\delta : (Q - \{ \qacc, \qrej \}) \times \Gamma \rightarrow \cP(Q \times \Gamma \times \{ L, R, N \})
\end{align*}
Again, when constructing a normal TM from a NTM (which is not required at the Midterm, or any other exam for that matter in this course),