1.9 State Machines - Invariants

For state machines, a derived variable is a _____, of real variables, that assigns a "value" to each state.

Exercise 1

  derivative sum function rule function 

Which of the following is a derived variable for the diagonal robot on the grid example?

Exercise 2

  x+y (mod 2) x y there are no derived variables x+y (mod 2) 

A derived variable is a constant iff it is both _____increasing and _____ decreasing.

Exercise 3

  strictly, strictly strictly, weakly weakly, weakly weakly, strictly weakly, weakly 

Termination of a state machine is guaranteed if it has a derived variable on \(\mathbb{N} \) that is _____ decreasing in any _____.

Exercise 4

  weakly, well ordered set strictly, well ordered set weakly, finite set strictly, finite set strictly, well ordered set