[MUSIC] A powerful model of a cyber physical component is given by a finer machine. Let us consider the following example of a system with three discrete modes. [SOUND]. We are going to consider letters for the modes, however one can use numbers or other type of symbols. The first mode will be A, the second mode will be B, and the third mode would be C. There will be inputs that are assigned to this system and that will allow this system mode to change from A to B, B to A, and so on. These transitions will be marked with these arrows. This would correspond when the input is equal to 0. There will be a transition from A to B when the input is equal to 1 and a transition from B to A when the input is equal to 0. And we can have also transitions from B to C when the input is equal to 1. And the mode of operation C is such that whenever a transition occurs will be mapped back to the mode C no matter what the input is. As you can see, the values allow for the input are either 0 or 1. And no matter where you start you can apply different input and transition between these modes. We will assume that the star mode in this particular example is mode A. So some of the features of this system are the following. We have finite, Number of states. The number of a states are 3 and we can actually define a set of a state which correlate these three different states. Similarly for the input, we have finite values of inputs. In this case there's only one input. And the inputs could be either 0 or 1. What one realizes is that, if someone gives you initial state in this case A one can given an input and that current initial state determine where the newer state will be, in some sort of a table. We can actually Capture these with a table where one of the columns is initial state. And then based on the input applied We can determine what the new value of this state could be. See we have two different values of the input. We can say that whenever the input on this denoted as V, is equal to 0 or when the input is equal to 1 we have different transitions. So, since we have only three states the possible initial states are A and B and C. And then, according to the value of the input that we apply, we will transition to a new state. So following this diagram, if we start in state A, and we apply input 0, this arrow suggests that we are going to have transition back to the same state. While if apply an input equal to 1 we will have transition to state B. When we start on the state B which we will correspond to putting this arrow in B. If you apply input 0 we will transition to state A. And if you were to apply input 1 we will transition to state C. And then as I mentioned before, no matter what input you apply when you are in C, you will go back to C. This table that you see right here, is the Transition Table. And holds not only for the initial state but any state that you might have along the ran. Meaning that if I give you a sequence of inputs 0, 1, 0, 1 one for instance, four values. And I stand in state A, what you can do following this table is when I apply 0, I go back to A, when I apply 1, I go to B. When I apply 0 again I go to A and when I apply 1, I go to B. So you an build the sequence of the states using these Transition table. [SOUND]
