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Movie Title Year Distributor Notes Rev Formats Career Bed 1969 Something Weird Video NonSex 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.[1] 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.[2] 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, and 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.[3] 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. FSMs are studied in the more general field of automata theory.
Contents 1 Example: coin-operated turnstile 2 Concepts and terminology 3 Representations 3.1 State/Event table 3.2 UML state machines 3.3 SDL state machines 3.4 Other state diagrams 4 Usage 5 Classification 5.1 Acceptors 5.2 Classifiers 5.3 Transducers 5.4 Sequencers 5.5 Determinism 6 Alternative semantics 7 Mathematical model 8 Optimization 9 Implementation 9.1 Hardware applications 9.2 Software applications 9.3 Finite-state machines and compilers 10 See also 11 References 12 Further reading 12.1 General 12.2 Finite-state machines (automata theory) in theoretical computer science 12.3 Abstract state machines in theoretical computer science 12.4 Machine learning using finite-state algorithms 12.5 Hardware engineering: state minimization and synthesis of sequential circuits 12.6 Finite Markov chain processes 13 External links

Example: coin-operated turnstile State diagram for a turnstile A turnstile An example of a simple mechanism that can be modeled by a state machine is a turnstile.[4][5] A turnstile, used to control access to subways and amusement park rides, is a gate with three rotating arms at waist height, one across the entryway. Initially the arms are locked, blocking the entry, preventing patrons from passing through. Depositing a coin or token in a slot on the turnstile unlocks the arms, allowing a single customer to push through. After the customer passes through, the arms are locked again until another coin is inserted. Considered as a state machine, the turnstile has two possible states: Locked and Unlocked.[4] There are two possible inputs that affect its state: putting a coin in the slot (coin) and pushing the arm (push). In the locked state, pushing on the arm has no effect; no matter how many times the input push is given, it stays in the locked state. Putting a coin in – that is, giving the machine a coin input – shifts the state from Locked to Unlocked. In the unlocked state, putting additional coins in has no effect; that is, giving additional coin inputs does not change the state. However, a customer pushing through the arms, giving a push input, shifts the state back to Locked. The turnstile state machine can be represented by a state-transition table, showing for each possible state, the transitions between them (based upon the inputs given to the machine) and the outputs resulting from each input: Current State Input Next State Output Locked coin Unlocked Unlocks the turnstile so that the customer can push through. push Locked None Unlocked coin Unlocked None push Locked When the customer has pushed through, locks the turnstile. The turnstile state machine can also be represented by a directed graph called a state diagram (above). Each state 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. An input that doesn't cause a change of state (such as a coin input in the Unlocked state) is 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. Concepts and terminology A state is a description of the status of a system that is waiting to execute a transition. A transition is a set of actions to be executed when a condition is fulfilled or when an event is received. For example, when using an audio system to listen to the radio (the system is in the "radio" state), receiving a "next" stimulus results in moving to the next station. When the system is in the "CD" state, the "next" stimulus results in moving to the next track. Identical stimuli trigger different actions depending on the current state. In some finite-state machine representations, it is also possible to associate actions with a state: an entry action: performed when entering the state, and an exit action: performed when exiting the state. Representations Fig. 1 UML state chart example (a toaster oven) Fig. 2 SDL state machine example Fig. 3 Example of a simple finite-state machine For an introduction, see State diagram. State/Event table Several state-transition table types are used. The most common representation is shown below: the combination of current state (e.g. B) and input (e.g. Y) shows the next state (e.g. C). The complete action's information is not directly described in the table and can only be added using footnotes. An FSM definition including the full actions information is possible using state tables (see also virtual finite-state machine). State-transition table Current state Input State A State B State C Input X ... ... ... Input Y ... State C ... Input Z ... ... ... UML state machines The Unified Modeling Language has a notation for describing state machines. UML state machines overcome the limitations of traditional finite-state machines while retaining their main benefits. UML state machines introduce the new concepts of hierarchically nested states and orthogonal regions, while extending the notion of actions. UML state machines have the characteristics of both Mealy machines and Moore machines. They support actions that depend on both the state of the system and the triggering event, as in Mealy machines, as well as entry and exit actions, which are associated with states rather than transitions, as in Moore machines.[citation needed] SDL state machines The Specification and Description Language is a standard from ITU that includes graphical symbols to describe actions in the transition: send an event receive an event start a timer cancel a timer start another concurrent state machine decision SDL embeds basic data types called "Abstract Data Types", an action language, and an execution semantic in order to make the finite-state machine executable.[citation needed] Other state diagrams There are a large number of variants to represent an FSM such as the one in figure 3. Usage In addition to their use in modeling reactive systems presented here, finite-state machines are significant in many different areas, including electrical engineering, linguistics, computer science, philosophy, biology, mathematics, video game programming, and logic. Finite-state machines are a class of automata studied in automata theory and the theory of computation. In computer science, finite-state machines are widely used in modeling of application behavior, design of hardware digital systems, software engineering, compilers, network protocols, and the study of computation and languages. Classification Finite-state machines can be subdivided into acceptors, classifiers, transducers and sequencers.[6] Acceptors Fig. 4: Acceptor FSM: parsing the string "nice". Fig. 5: Representation of an acceptor; this example shows one that determines whether a binary number has an even number of 0s, where S1 is an accepting state and S2 is a non accepting state. Acceptors (also called detectors or recognizers) produce binary output, indicating whether or not the received input is accepted. Each state of an acceptor is either accepting or non accepting. Once all input has been received, if the current state is an accepting state, the input is accepted; otherwise it is rejected. As a rule, input is a sequence of symbols (characters); actions are not used. The start state can also be an accepting state, in which case the acceptor accepts the empty string. The example in figure 4 shows an acceptor that accepts the string "nice". In this acceptor, the only accepting state is state 7. A (possibly infinite) set of symbol sequences, called a formal language, is a regular language if there is some acceptor that accepts exactly that set. For example, the set of binary strings with an even number of zeroes is a regular language (cf. Fig. 5), while the set of all strings whose length is a prime number is not.[7]:18,71 An acceptor could also be described as defining a language that would contain every string accepted by the acceptor but none of the rejected ones; that language is accepted by the acceptor. By definition, the languages accepted by acceptors are the regular languages. The problem of determining the language accepted by a given acceptor is an instance of the algebraic path problem—itself a generalization of the shortest path problem to graphs with edges weighted by the elements of an (arbitrary) semiring.[8][9][jargon] An example of an accepting state appears in Fig. 5: a deterministic finite automaton (DFA) that detects whether the binary input string contains an even number of 0s. S1 (which is also the start state) indicates the state at which an even number of 0s has been input. S1 is therefore an accepting

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