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authorErin van der Veen2018-04-10 15:19:29 +0200
committerErin van der Veen2018-04-10 15:19:29 +0200
commitdff0d9ab2507fac388784308099eafa2e225bff3 (patch)
treec83d7c0aa7362d8cb4e7c9088767128d62afb089 /Assignment1
parentDefinitions do change, change definitions (diff)
Define equivalence for LTLP
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\end{matrix*}
$$
+Now that we have defined the formal semantics of LTLP,
+we can define equivalence on LTLP formulas.
+\begin{definition}
+ LTLP formulae $\phi_1,\phi_2$ are equivalent, denoted $\phi_1 \equiv \phi_2$ iff they verify the following property:
+ $$\text{for any path } \pi \text{ and any position } i, \pi, i \vDash \phi \Leftrightarrow \pi, i \vDash \psi$$.
+\end{definition}
+
+Additionally, we can define another form of equivalence, initial equivalence:
+\begin{definition}
+ LTLP formulae $\phi_1,\phi_2$ are initial equivalent, denoted $\phi_1 \equiv_0 \phi_2$ iff they verify the following property:
+ $$\text{for any path } \pi, \pi, 0 \vDash \phi \Leftrightarrow \pi, 0 \vDash \psi$$.
+\end{definition}
+
\subsection{LTL and LTL-Past}
%TODO: Consider/Analyse differences between LTL and LTL-Past