1.9 State Machines - Invariants

What are the states in the Die Hard example?

Exercise 1

  the total amount of water in the two jugs the amount of water in jugs: \((b, l) \), where \(b \) is the amount in the big jug, \(l \) is the amount in the small jug the difference in the amount of water in the two jubs none of the above the amount of water in jugs: \((b, l) \), where \(b \) is the amount in the big jug, \(l \) is the amount in the small jug 

The preserved invariant for the state machine in the Die Hard Once For All example is:

Exercise 2

  The total amount of water must increase or decrease by exactly three gallons. The total amount of water must be preserved. The number of gallons in each jug is never divisible by the difference of the jugs. The number of gallons in each jug is always divisible by three. The number of gallons in each jug can be any integer value. The number of gallons in each jug is always divisible by three. 

Which of the following are valid states for the robot's location in the Diagonal Robot example?

Exercise 3

 (-11, 3) 

 (3, 7) 

 (5, 4) 

 (2, 1) 

Which of the following is true about Floyd's Invariant Principle?

Exercise 4

 It is induction reformulated for state machines. 

 For a preserved invariant \(P(\text{state}) \), if \(P(\text{start state}) \), then \(P(r) \), for all reachable states \(r \) . 

 Preserved invariants are the same as invariants. 

 Any preserved invariant of a state machine is a property of the states, including the final state, if any.