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author | Erin van der Veen | 2018-04-10 15:19:29 +0200 |
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committer | Erin van der Veen | 2018-04-10 15:19:29 +0200 |
commit | dff0d9ab2507fac388784308099eafa2e225bff3 (patch) | |
tree | c83d7c0aa7362d8cb4e7c9088767128d62afb089 /Assignment1 | |
parent | Definitions do change, change definitions (diff) |
Define equivalence for LTLP
Diffstat (limited to 'Assignment1')
-rw-r--r-- | Assignment1/assignment1.tex | 13 |
1 files changed, 13 insertions, 0 deletions
diff --git a/Assignment1/assignment1.tex b/Assignment1/assignment1.tex index 03b80d0..1e50572 100644 --- a/Assignment1/assignment1.tex +++ b/Assignment1/assignment1.tex @@ -186,6 +186,19 @@ $$ \end{matrix*} $$ +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 |