Correct Answer.
We determine the meaning of the CTL formula AG (p 
A[q U r]) by
- breaking it up into significant subformulas,
- determining the meaning of these subformulas, and by
- determining the meaning of the entire formula by composing the meanings
of subformulas in the manner suggested by the logic operators
that are present.
To wit,
- the meaning of A[q U r] at any state s is that 'for all computation paths
that begin in s, the predicate q is true until the path reaches a state in
which r is true (and such a state has to be reached)'.
- The meaning of p A[q U r] at
any state s is that 'if p holds in state s, then A[q U r] has to hold at
state s as well'.
- The meaning of AG(p A[q U r]) at
any state s is that 'p A[q U r] holds
at any state t that is reachable from state s'.
The English specification "For any reachable state in which p is true, then, on any path from that state, q is continuously true until r becomes true, and r isguaranteed to become true" is just re-expressing the meaning of
AG(p A[q U r]) that we uncovered.
Note that "on any path from that state" expresses "reachable" and that
"r isguaranteed to become true" reflects the aspect of "q U r" which insists
on r being true eventually.
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