Answer to Question #15441 in Discrete Mathematics for suresh rajkumar
explain why a finite automaton does or does not correspond to a graph
A finite-state machine (FSM) or finite-state automaton (plural: automata), or simply a state machine, is a mathematical model of computation used to design both computer programs and sequential logic circuits. It is conceived as an abstract machine that can be in one of a finite number of states. The machine is in only one state at a time; the state it is in at any given time is called the current state. It can change from one state to another when initiated by a triggering event or condition, this is called a transition. A particular FSM is defined by a list of its states, and the triggering condition for each transition.
It can also be represented by a directed graph called a state diagram (above). Each of the states is represented by a node (circle). Edges (arrows) show the transitions from one state to another. Each arrow is labeled with the input that triggers that transition. Inputs that don't cause a change of state (such as a coin input in the Unlocked state) are represented by a circular arrow returning to the original state. The arrow into the Locked node from the black dot indicates it is the initial state.