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+This is pdfTeX, Version 3.141592653-2.6-1.40.26 (TeX Live 2024/Arch Linux) (preloaded format=pdflatex 2024.7.2)  18 NOV 2024 14:49
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 ts/enc/dvips/base/8r.enc}
 
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-(./sections/attacker_models.tex) (./sections/case_studies.tex
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 []\OT1/ptm/m/n/10 In the Pro-cess: $\OML/cmm/m/it/10 s[]; s[]; s[]; []$ \OT1/pt
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 1/ptm/m/n/10 and
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 LaTeX Font Warning: Font shape `OT1/ptm/m/scit' undefined
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 \OT1/ptm/m/n/10 via the pre-vi-ous the-o-rem we can con-struct B[]uchi Au-
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 LaTeX2e <2023-11-01> patch level 1
 L3 programming layer <2024-02-20>
  ***********
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-Output written on ./main.pdf (7 pages, 273739 bytes).
+Output written on main.pdf (7 pages, 274184 bytes).
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sections/appendix.tex

@@ -37,13 +37,19 @@ A transition \( (s, x, s') \in T \) is called an \emph{input transition} if \( x
 Given a \ba \( B = (Q, \Sigma, \delta, Q_0, F) \), we construct a corresponding Process \( P = \langle AP, I, O, S, s_0, T, L \rangle \) as follows:
 
 \begin{itemize}
-    \item {Atomic Propositions: \( AP = \{ \text{accept} \} \), a singleton set containing a special proposition indicating acceptance.
+    \item Atomic Propositions: \( AP = \{ \text{accept} \} \), a singleton set containing a special proposition indicating acceptance.
     \item Inputs and Outputs: \( I = \Sigma \) and \( O = \emptyset \).
     \item States: \( S = Q \) and \( s_0 \in Q_0 \).
     \item Transition Relation: \( T = \delta \).
     \item Labeling Function: \( L: S \to 2^{AP} \) defined by
-    \[        L(s) = \begin{cases}            \{ \text{accept} \} & \text{if } s \in F, \\            \emptyset & \text{otherwise}.        \end{cases}    \]
 \end{itemize}
+\[        
+  L(s) = 
+  \begin{cases}            
+  \{ \text{accept} \} & \text{if } s \in F, \\            
+  \emptyset & \text{otherwise}.        
+  \end{cases}    
+\]
 
 In this mapping, the states and transitions of the BA are preserved in the Process, and the accepting states \( F \) are identified via the labeling function \( L \).