# Answer to Question #15441 in Discrete Mathematics for suresh rajkumar

Question #15441

explain why a finite automaton does or does not correspond to a graph

Expert's answer

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.

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.

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