# 1.9 State Machines - Invariants

## Derived Variables and Termination

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

Exercise 1
2. Which of the following is a derived variable for the diagonal robot on the grid example?

Exercise 2
3. A derived variable is a constant iff it is both _____increasing and _____ decreasing.

Exercise 3
4. Termination of a state machine is guaranteed if it has a derived variable on $$\mathbb{N}$$ that is _____ decreasing in any _____.

Exercise 4