linear temporal logic
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LINEAR TEMPORAL LOGIC
Fall 2013Dr. Eric Rozier
Propositional Temporal Logic
Does the following hold?
yes
Propositional Temporal Logic
Does the following hold?
no
Examples: What do they mean?
G F pp holds infinitely often
F G pEventually, 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
Remember:Gp p holds in all statesFp p holds eventuallyXp p holds in the next state
Examples: Write in Temporal Logic
1. “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)
2. “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)
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.
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.
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.
What does this property mean?
• F(p => Xq)
• Is it satisfied by this trace?
p -> p -> p -> __ -> q -> p -> …
What does this property mean?
• F(p => Xq)
• Is it satisfied by this trace?
p -> p -> p -> __ -> q -> p -> q -> …
Does this automaton satisfy the property?
• pUq
Does this automaton satisfy the property?
• pUq
Does this automaton satisfy the property?
• qRp
Does this automaton satisfy the property?
• qRp
Does this automaton satisfy the property?
• qRp
Does this automaton satisfy the property?
• qRp
Does this automaton satisfy the property?
• F(p & XXX !q)
Does this automaton satisfy the property?
• F(p & XXX !q)
Does this automaton satisfy the property?
• F(p & XXX !q)
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