update

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 \( L \).