Incorrect 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 "If p is true in every reachable state, then on every path there is a state at which r is true, and q is true continuously until then" is a far
cry from the meaning of the formula above.
The premise "p is true in every reachable state" can be modeled by
AG(p). The conclusion "on every path there is a state at which r is true, and q is true continuously until then" may be expressed by the CTL formula
A(q U r).
Thus, the English language specification is modeled by the
CTL formula
AG(p) A(q U r). Although this
formula looks similar to the given AG(p A[q U r]), it has a dramatically different meaning.
For example, consider a state s in a model where each state t, reachable
from s, satisfies p. Then the former formula insists that all computation
paths beginning in s satisfy "q U r",
whereas the latter formula
insists on A[q U r] to hold at all reachable states t, for p holds for
all of them, thereby "triggering" the implication!
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