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# 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
1
2012-10-02T07:19:21-0400
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&#039;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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