Source : Free On-Line Dictionary of Computing

Finite State Machine
     
         (FSM or "Finite State
        Automaton", "transducer") An {abstract machine} consisting of
        a set of {states} (including the initial state), a set of
        input events, a set of output events, and a state transition
        function.  The function takes the current state and an input
        event and returns the new set of output events and the next
        state.  Some states may be designated as "terminal states".
        The state machine can also be viewed as a function which maps
        an ordered sequence of input events into a corresponding
        sequence of (sets of) output events.
     
        A {deterministic} FSM (DFA) is one where the next state is
        uniquely determinied by a single input event.  The next state
        of a {nondeterministic} FSM (NFA) depends not only on the
        current input event, but also on an arbitrary number of
        subsequent input events.  Until these subsequent events occur
        it is not possible to determine which state the machine is in.
     
        It is possible to automatically translate any nondeterministic
        FSM into a deterministic one which will produce the same
        output given the same input.  Each state in the DFA represents
        the set of states the NFA might be in at a given time.
     
        In a probabilistic FSM [proper name?], there is a
        predetermined {probability} of each next state given the
        current state and input (compare {Markov chain}).
     
        The terms "acceptor" and "transducer" are used particularly in
        language theory where automata are often considered as
        {abstract machines} capable of recognising a language (certain
        sequences of input events).  An acceptor has a single
        {Boolean} output and accepts or rejects the input sequence by
        outputting true or false respectively, whereas a transducer
        translates the input into a sequence of output events.
     
        FSMs are used in {computability theory} and in some practical
        applications such as {regular expressions} and digital logic
        design.
     
        See also {state transition diagram}, {Turing Machine}.
     
        [J.H. Conway, "regular algebra and finite machines", 1971, Eds
        Chapman & Hall].
     
        [S.C. Kleene, "Representation of events in nerve nets and
        finite automata", 1956, Automata Studies. Princeton].
     
        [Hopcroft & Ullman, 1979, "Introduction to automata theory,
        languages and computations", Addison-Wesley].
     
        [M. Crochemore "tranducters and repetitions",
        Theoritical. Comp. Sc. 46, 1986].
     
        (2001-09-22)