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[TI] Compact: Add better explanation

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Janis Hutz
2025-11-04 15:57:36 +01:00
parent 22b131efd7
commit 19ca631705
4 changed files with 15 additions and 14 deletions
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semester3/ti-compact/parts/02_finite-automata.tex
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@@ -20,7 +20,7 @@ We can note the automata using graphical notation similar to graphs or as a seri
\item $\delta(q, a) = p$ transition from $q$ on reading $a$ to $p$
\item $q_0$ initial state
\item $F \subseteq Q$ accepting states
\item $\mathcal{L}_{EA}$ regular languages (accepted by FA)
\item $\cL_{EA}$ regular languages (accepted by FA)
\end{itemize}
\end{multicols}
@@ -144,7 +144,7 @@ Thus, all four words have to lay in pairwise distinct states and we thus need at
\subsection{Non-determinism}
The most notable differences between deterministic and non-deterministic FA is that the transition function maps is different: $\delta: Q \times \Sigma \rightarrow \mathcal{P}(Q)$.
The most notable differences between deterministic and non-deterministic FA is that the transition function maps is different: $\delta: Q \times \Sigma \rightarrow \cP(Q)$.
I.e., there can be any number of transitions for one symbol from $\Sigma$ from each state.
This is (in graphical notation) represented by arrows that have the same label going to different nodes.
@@ -162,5 +162,5 @@ States are no now sets of states of the NFA in which the NFA could be in after p
For each state, the set of states $P = \hdelta(q_0, z)$ for $|z| = n$ represents all possible states that the NFA could be in after doing the first $n$ calculations.
Correspondingly, we add new states if there is no other state that is in the same branch of the calculation tree $\mathcal{B}_M(x)$.
Correspondingly, we add new states if there is no other state that is in the same branch of the calculation tree $\cB_M(x)$.
So, in other words, we execute BFS on the calculation tree.