[Bobs Explains the transitive function]
Bob: The transition function defines the rules for moving. We can use our light bulb switch as an example of finite automata. Suppose in the off state, if the input is ON, then the state of the light bulb will shift towards ON, right? And in the ON state, if the input is OFF, then the state of the light bulb will shift towards OFF. So if we denote OFF input by 0 and ON input by 1, now we can show this using the transition function δ(ON, 0) = OFF or δ(OFF, 1) = ON. I hope you are getting my point, Alice. This means that here, delta is showing what the input will be to move towards a particular state.
Alice: Okay, so does the delta or transition function show the rule that determines what input will cause a move to a particular state, right?
Bob: Exactly, Alice. The transition function, often denoted by ( δ ), specifies the conditions under which a transition occurs from one state to another in a finite automaton. It’s a formal way to express the rules that govern the state changes. So, in the context of the light bulb example:
When the light bulb is OFF and the input is 1 (representing the ON switch), the transition function (δ(OFF, 1)) will result in the light bulb state changing to ON.
Conversely, when the light bulb is ON and the input is 0 (representing the OFF switch), the transition function (δ(ON, 0)) will result in the light bulb state changing to OFF.
Alice: Now, I got you.
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