# Finite State Machine

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Related to Accepting state: State transition function

## Finite State Machine

(mathematics, algorithm, theory)
(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].
References in periodicals archive ?
In this model, (i) for each accepted input, A has at least one computation path halting in an accepting state and, moreover, no path halts in a rejecting state, (ii) for each rejected input, A has at least one computation path halting in a rejecting state and, moreover, no path halts in an accepting state.
Joliet is planning to transfer foster children from Catholic Charities to different agencies while Springfield has decided to stop accepting state funds for foster care and continue the service on its own dime.
After all our trading partners in Europe have no difficulty in accepting state ownership that competes in the market place.
Basically, they provided for formation of a not-for-profit entity in this case, Strandberg and Rodvik said, more of a custom-designed corporation with broad responsibility for keeping the lights on and dealing in billions of dollars in utility projects, notably including borrowing money and accepting State appropriations.
24) For example, Article 121(5) may be read to exempt nationals of non-accepting States Parties from prosecution for the crime of aggression, even if committed on the territory of an accepting State Party.
A waiting period, however, would ease doubts about lawmakers' motivations in accepting state jobs.
This summer, the Department of Education begins accepting state applications for the federal government's largest one-time investment in K-12 public school reform.
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Ruane said that when the ruling was made 10 days ago, the men were "faced with the decision of accepting state security or making their own arrangements".
His first step was accepting state and regional government relations responsibilities for the Appraisal Institute, followed by becoming nationally active by working with the Region X state lobbyist, the national Government Relations Committee and the Washington, D.
5 standard, it ordered the agency to do more work on the ozone standard and 2) as the implementation plan shows, EPA will have some leeway in designating non-attainment areas and accepting state plans.
This kind of accepting state of mind for "favorable" beliefs is not going to help our argument that humanism depends on unfettered inquiry and reason.

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