state machines - definition. What is state machines
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MATHEMATICAL MODEL OF COMPUTATION; ABSTRACT MACHINE THAT CAN BE IN EXACTLY ONE OF A FINITE NUMBER OF STATES AT ANY GIVEN TIME
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  • TTL]] counter, a type of state machine
  • Fig. 5: Representation of an acceptor; this example shows one that determines whether a binary number has an even number of 0s, where ''S''<sub>1</sub> is an ''accepting state'' and ''S''<sub>2</sub> is a ''non accepting state''.
  • Fig. 3 Example of a simple finite-state machine
  • Fig. 6 Transducer FSM: Moore model example
  • Fig. 7 Transducer FSM: Mealy model example
  • Fig. 4: Acceptor FSM: parsing the string "nice".
  • Fig. 2 SDL state machine example
  • A turnstile
  • State diagram for a turnstile
  • Fig. 1 UML state chart example (a toaster oven)

state machine         
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 [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)
Finite-state machine         
A finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of states at any given time.

ويكيبيديا

Finite-state machine

A finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of states at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a transition. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. Finite-state machines are of two types—deterministic finite-state machines and non-deterministic finite-state machines. A deterministic finite-state machine can be constructed equivalent to any non-deterministic one.

The behavior of state machines can be observed in many devices in modern society that perform a predetermined sequence of actions depending on a sequence of events with which they are presented. Simple examples are: vending machines, which dispense products when the proper combination of coins is deposited; elevators, whose sequence of stops is determined by the floors requested by riders; traffic lights, which change sequence when cars are waiting; combination locks, which require the input of a sequence of numbers in the proper order.

The finite-state machine has less computational power than some other models of computation such as the Turing machine. The computational power distinction means there are computational tasks that a Turing machine can do but an FSM cannot. This is because an FSM's memory is limited by the number of states it has. A finite-state machine has the same computational power as a Turing machine that is restricted such that its head may only perform "read" operations, and always has to move from left to right. FSMs are studied in the more general field of automata theory.