The LTL formula AF (p Xp) cannot be expressed in CTL
We want to prove that for all CTL formula and i 1,
() | | i (Mi , ai |= Ni , ai |= ).
Note that () implies that for all i 1,
() | | i (Mi+1 , bi+1 |= Ni+1 , bi+1 |= ).
We prove () by an induction on | |
A winning strategy for Player I
We prove that for all states w W and w W , if (w, w ) Hi , then
L(w) = L (w ) or Player I has a strategy to win a game that starts in
position (w, w ) in at most i rounds.
Note (this requires some thinking) that this indeed
Formal Verication of Reactive Systems
Temporal Logic
The logic LTL is a linear temporal logic. Formulas of LTL are constructed from a set AP of atomic proposition using the usual Boolean operators and the temporal operators X (next time) and U (until). Fo
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The temporal logic LTL
The logic LTL is a linear temporal logic. Formulas of LTL are constructed
from a set AP of atomic propositions using the usual Boolean operators and
the temporal operators X (next time) and U (until). Formally, an LTL
formula over