From e01166bfedcd8351e00ded1d94f49125ed03f715 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Sun, 5 Oct 2025 07:20:03 +0200 Subject: [PATCH] [TI] Add some intuition for classes --- .../02_finite-automata/00_representation.tex | 4 ++++ semester3/ti/ti-summary.pdf | Bin 851961 -> 852374 bytes 2 files changed, 4 insertions(+) diff --git a/semester3/ti/parts/02_finite-automata/00_representation.tex b/semester3/ti/parts/02_finite-automata/00_representation.tex index d7dd767..fbc5b2e 100644 --- a/semester3/ti/parts/02_finite-automata/00_representation.tex +++ b/semester3/ti/parts/02_finite-automata/00_representation.tex @@ -93,6 +93,10 @@ Also gilt $L(M) = \{ w \in \Sigma^* \divides (q_0, w) \bigvdash{M}{*} (p, \lambd Jeder EA teilt die Menge $\Sigma^*$ in $|Q|$ Klassen $\text{Kl}[p] = \{ w \in \Sigma^* \divides \hat{\delta}(q_0, w) = p \} = \{ w \in \Sigma^* \divides (q_0, w) \bigvdash{M}{*} (p, \lambda) \}$ und entsprechend $\bigcup_{p \in Q} \text{Kl}[p] = \Sigma^*$ und $\text{Kl}[p] \text{Kl}[q] = \emptyset \smallhspace \forall p \neq q \in Q$. + +\shade{Cyan}{Intuition}: Die Klassen sind Mengen, die hier Wörter mit gewissen Eigenschaften, die der EA bestimmt hat, wenn er in Zustand $q_i$ endet, enthalten. +Diese Eigenschaften sind beispielsweise, dass alle Wörter, für die der EA in Zustand $q_i$ endet mit einer gewissen Sequenz enden, sie einen gewissen Zahlenwert haben, etc. + In dieser Terminologie gilt dann $L(M) = \bigcup_{p \in F} \text{Kl}[p]$. 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