1. LINEAR TEMPORAL LOGIC
Fall 2013
Dr. Eric Rozier

2. Propositional Temporal Logic
Does the following hold?
yes

3. Propositional Temporal Logic
Does the following hold? no

4. Examples: What do they mean?
Remember:
Gp p holds in all states
Fp p holds eventually
Xp p holds in the next state
G F p
p holds infinitely often
F G p
Eventually, p holds henceforth
G( p => F q )
Every p is eventually followed by a q
F( p => (X X q) )
Every p is followed by a q two reactions later

5. Examples: Write in Temporal Logic
“Whenever the iRobot is at the ramp-edge (cliff), eventually it moves 5 cm away from the cliff.”
p – iRobot is at the cliff
q – iRobot is 5 cm away from the cliff
G (p => F q)
“Whenever the distance between cars is less than 2m, cruise control is deactivated”
p – distance between cars is less than 2 m
q – cruise control is active
G (p => X ! q)
1. G (p => F q)
2. G (p => X \neg q)

6. Remember, LTL Formulas are Formulas
Suppose the robot must visit a set of n locations l1, l2, …, ln. Let pi be an atomic formula that is true if and only if the robot visits location li.
Express the following:
The robot must eventually visit at least one of the n locations.

7. Remember, LTL Formulas are Formulas
Suppose the robot must visit a set of n locations l1, l2, …, ln. Let pi be an atomic formula that is true if and only if the robot visits location li.
Express the following:
The robot must eventually visit all n locations, but in any order.

8. Remember, LTL Formulas are Formulas
Suppose the robot must visit a set of n locations l1, l2, …, ln. Let pi be an atomic formula that is true if and only if the robot visits location li.
Express the following:
The robot must eventually visit all n locations, in numeric order.

9. What does this property mean?
F(p => Xq)
Is it satisfied by this trace?
p -> p -> p -> __ -> q -> p -> …

10. What does this property mean?
F(p => Xq)
Is it satisfied by this trace?
p -> p -> p -> __ -> q -> p -> q -> …

11. Does this automaton satisfy the property?
pUq

12. Does this automaton satisfy the property?
pUq

13. Does this automaton satisfy the property?
qRp

14. Does this automaton satisfy the property?
qRp

15. Does this automaton satisfy the property?
qRp

16. Does this automaton satisfy the property?
qRp

17. Does this automaton satisfy the property?
F(p & XXX !q)

18. Does this automaton satisfy the property?
F(p & XXX !q)

19. Does this automaton satisfy the property?
F(p & XXX !q)