INTRODUCTION TO: SOFTWARE TESTING

For the following questions (a)–(c), consider the method FSM for a (simpli- fied) programmable thermostat. Suppose the variables that define the state and the methods that transition between states are:

partOfDay : {Wake, Sleep} temp : {Low, High}

// Initially "Wake" at "Low" temperature

// Effects: Advance to next part of day public void advance();

// Effects: Make current temp higher, if possible public void up();

// Effects: Make current temp lower, if possible public void down();

1. (a)  How many states are there?

b)In this problem we will generalize the idea used in part(a). Let there be n state variables X1, X2, . . . , Xn. Each state variable Xi can take mi possible distinct values. In worst case how many states are required for designing the finite state machine? Do not consider any kind of state minimization.

1.  Hint: A good way to start is to play with small examples. You may consider, for instance, n = 3 and m1 = 2, m2 = 3, m3 = 2. Try to work out manually in this case that how many states are required in worst case.