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LINEAR TEMPORAL LOGIC

LINEAR TEMPORAL LOGIC. Fall 2013 Dr. Eric Rozier. Propositional Temporal Logic. Does the following hold?. yes. Propositional Temporal Logic. Does the following hold?. no. G F p p holds infinitely often F G p Eventually, p holds henceforth G ( p => F q )

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LINEAR TEMPORAL LOGIC

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

  5. “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) Examples: Write in Temporal Logic

  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)

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