(mathematics, algorithm, theory) | **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 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]. | |