more

sections/proofs.tex

@@ -74,8 +74,7 @@ In both structures, a run is an infinite sequence of states connected by transit
 \end{itemize}
 
 An accepting run in the \ba visits states in \( F \) infinitely often. Similarly, an accepting run in the Process visits states labeled with \( p \) infinitely often. Since \( F = \{ s \in S \mid p \in L(s) \} \), the acceptance conditions are preserved under the mappings.
-  
-\end{proof}
+  \end{proof}
 
 \begin{definition}[Threat Model]
 A threat model is a tuple \( (P, (Q_i)_{i=0}^m, \phi) \) where:
@@ -104,10 +103,11 @@ A threat model is a tuple \( (P, (Q_i)_{i=0}^m, \phi) \) where:
   \[
     \left(BA_{P} \mid \mid BA_{\text{Daisy}(Q_0)} \mid \mid \ldots \mid \mid BA_{\text{Daisy}(Q_m)}\right) \subseteq BA_{\phi}
   \] 
+Where rendezvous composition for I/O \ba is precise the same as for I/O Kripke Automata; that is, input and output transitions are matched. It's easy to see these composition operations are equivalent.
 \end{proof}
 
 \begin{theorem}
-  Checking whether there exists an attacker for a given threat model, the R-$\exists$ASP problem as proposed in \cite{Hippel2022_anonym}, is PSPACE-complete.
+  Checking whether there exists an attacker for a given threat model, the R-$\exists$ASP problem as proposed in \cite{Hippel2022_anonym}, is in PSPACE.
 \end{theorem}
 
 \begin{proof}