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Topic: Finite automaton

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Automata theory

Deterministic finite state machine

Pushdown automaton

Turing machine

Nondeterministic finite state machine

Regular language

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	PlanetMath: deterministic finite automaton
		Although the operation of a DFA is much easier to compute than that of a non-deterministic automaton, it is non-trivial to directly generate a DFA from a regular grammar.
		It is much easier to generate a non-deterministic finite automaton from the regular grammar, and then transform the non-deterministic finite automaton into a DFA.
		This is version 6 of deterministic finite automaton, born on 2002-02-24, modified 2007-09-28.
	www.planetmath.org /encyclopedia/DeterministicFiniteAutomaton.html (502 words)

	Finite state machine
		A finite state machine (FSM) or finite state automaton (FSA) is an abstract machine used in the study of computation and languages that has only a finite, constant amount of memory (the state).
		Finite automata may operate on languages of finite words (the standard case), infinite words (Rabin automata, Büchi automata[?]), or various types of trees (tree automata), to name the most important cases.
		Apart from theory, finite state machines occur also in hardware circuits, where the input, the state and the output are bit vectors of fixed size (Moore and Mealy machines).
	www.ebroadcast.com.au /lookup/encyclopedia/fs/FSM.html (830 words)

	NationMaster - Encyclopedia: Deterministic finite state machine
		In the theory of computation, a deterministic finite state machine or deterministic finite automaton (DFA) is a finite state machine where for each pair of state and input symbol there is one and only one transition to a next state.
		The state diagram for M is: In Automata Theory, a state transition table is a table describing the transition function T of a finite automaton.
		Finite state machines are one type of the automata studied in automata theory and the theory of computation.
	www.nationmaster.com /encyclopedia/Deterministic-finite-state-machine (1480 words)

	Informal Essays: Iterated Finite Automata
		Any finite automaton can be represented by a network, in which each node is a state, and each edge represents a transition from one state to another (see e.g.
		These days the most common type of finite automaton considered are recognizer finite automata, in which there is a single symbol (say 0 or 1) on a given edge.
		Transducer finite automata are sometimes known as Mealy machines, and particularly in the past, they were often used as models of electrical or mechanical machines that operate in a sequential way.
	www.stephenwolfram.com /publications/informalessays/iteratedfinite (1575 words)

	Finite Automata
		A reduced automaton is used to represent the ``discernable'' structure of a dynamical system; you cannot expect a learner to discern the difference between two states if no sequence of inputs and outputs serves to distinguish them.
		In a stochastic finite automaton (SFA), f(q,a) and h(q) are random functions and Pr(f(q,a)q,a) and Pr(h(q)) define the state transition and output probabilities respectively.
		In a probabilistic finite automata (PFA), the output in state q is a random function of q, and the state following q is a deterministic function of q and the output in q.
	www.cs.brown.edu /research/ai/dynamics/tutorial/Documents/FiniteAutomata.html (0 words)

	[No title] (Site not responding. Last check: )
		Finite automata recognize regular languages and, conversely, any language that is recognized by a finite automaton is regular.
		If the finite automaton is in an accepting state when the input ceases to come, the sequence of input symbols given to the finite automaton is "accepted".
		There is a finite control which determines the state of the automaton and also controls the movement of the head.
	www.cs.odu.edu /~toida/nerzic/390teched/regular/fa/dfa-definitions.html (892 words)

	James Mc Parlane's Blog - Finite State Automata - The State Of The Art
		On this view, the automaton generates a formal language, which is a set of strings.
		The two views of automata are equivalent: the function that the automaton computes is precisely the characteristic function of the set of strings it recognized.
		The class of languages generated by finite automata is known as the class of regular languages.
	blog.metawrap.com /blog/FiniteStateAutomataTheStateOfTheArt.aspx (1220 words)

	Alternating finite automaton
		In automata theory, an alternating finite automaton (AFA) is a non-deterministic finite automaton whose transitions are divided into existential and universal transitions.
		For a transition, A nondeterministically chooses to switch the state to either or, reading a.
		A basic theorem tells that any AFA is equivalent to an non-deterministic finite automaton (NFA) by performing a similar kind of powerset construction as it is used for the transformation of a NFA to a deterministic finite automaton (DFA).
	www.xasa.com /wiki/en/wikipedia/a/al/alternating_finite_automaton.html (160 words)

	Linear-bounded automaton@Everything2.com
		The regular language is recognized by a regular expression or finite state automaton (they are ultimately the same thing).
		A context free language is recognized by a pushdown automaton which is a finite state automaton with a stack.
		The linear-bounded automaton (lba) is a Turing Machine with a tape of some finite length.
	www.everything2.com /index.pl?node_id=1394039 (802 words)

	Finite state machine Summary
		Intuitively a finite automaton is a mathematical model of computing device that has discrete inputs and outputs as well as a finite set of internal states.
		A finite state machine (FSM) or finite automaton is a model of behavior composed of states, transitions and actions.
		Finite state machines are one type of the automata studied in automata theory and the theory of computation.
	www.bookrags.com /Finite_state_machine (3181 words)

	CSCI 172 99f Lab 4: Finite Automata (Site not responding. Last check: )
		A Finite State Automaton is a machine that eats input and changes internal state based on its current state and the input it just ate.
		Draw a finite state automaton to determine if a given string of characters is a legal C++ identifier.
		Draw a finite state automaton that has two states, "ignore" and "output." The automaton should start in the "output" state and moves to the ignore state whenever it encounters an html tag, then back to the output state when the html tag has completed.
	www.cs.xu.edu /csci172/99f/lab4 (306 words)

	A Finite Automaton Example (Site not responding. Last check: )
		So to put it in another way, A finite automaton is essentially a machine that performs a certain task.
		This sort of machine is often called a finite state machine; this is because the machine has a number of states, one of which is an initial state.
		Finite automata can also be used to do other things than accept or reject input strings.
	gaia.ecs.csus.edu /~automata/fa-example.html (595 words)

	Basics of Automata Theory
		Automatons are abstract models of machines that perform computations on an input by moving through a series of states or configurations.
		Each state accepts a finite number of inputs, and each state has rules that describe the action of the machine for ever input, represented in the state transition mapping function.
		They can operate on languages with a finite number of words (standard case), an infinite number of words (Rabin automata, Bïrche automata), various types of trees, and in hardware circuits, where the input, the state and the output are bit vectors of a fixed size.
	www.stanford.edu /~jcackler/automata/basics.htm (1640 words)

	Pushdown automaton
		Informally, a pushdown automaton is a finite automaton outfitted with access to a potentially unlimited amount of memory in the form of a single stack.
		The finite automaton in question is usually a Nondeterministic finite state machine (resulting in a nondeterministic pushdown automaton or NPDA) since deterministic pushdown automata cannot recognize all context-free languages.
		If we allow a finite automaton access to two stacks instead of just one, we obtain a more powerful device - equivalent in power to a Turing machine.
	www.xasa.com /wiki/en/wikipedia/p/pu/pushdown_automaton.html (267 words)

	LANGUAGES, GRAMMARS, AUTOMATA & QUANTUM ANALOGS
		Finite State Machine (FSA) is a sequential machine with a Q of finite cardinality.
		Automaton An automaton is the heart of a sequential machine, that which deals only with inputs and states.
		And part of the definition of a push down automaton is a symmetry requirement on the transition relation H to the effect that if (q, v) → (r, vs) on a word z then (q, v') → (r, v's) on the word z for all other stack words v'.
	graham.main.nc.us /~bhammel/MATH/autom.html (4505 words)

	Finite-State Automata
		In the case of an automaton that is equivalent to a finite grammar, as is the case for the transition network illustrated here, the nodes are labelled with the nonterminal symbols of the grammar.
		In a transition network diagram for an automaton that is equivalent to a finite grammar, the arcs are labelled with the words from the terminal vocabulary of the grammar.
		An automaton is said to be nondeterministic if its transition function is multi-valued, that is, there are at least two transitions with the same current state and input symbol pair, but with different new states.
	web.uvic.ca /~ling48x/ling484/notes/fsa.html (2176 words)

	The Finite Nature Hypothesis of Edward Fredkin
		Fredkin concludes: "Given Finite Nature, what we have at the bottom is a Cellular Automaton of some kind." And, because "Automata, Cellular Automata and Finite State Machines are all forms of computers," this is to say that at the bottom of the physics of the natural world, we have a computer of some kind.
		Accordingly, this process whereby the cellular automaton is "computing its future as fast as possible" effectively mimics "the apparent randomness of quantum mechanical processes" and satisfies the condition that the result should be random in the sense that it is unknowable even in principle.
		Finite Nature means that our world operates as though it were the product of a computing system, and Fredkin sees that this is because our universe is an artifact produced by a computer of some sort.
	www.bottomlayer.com /bottom/finite-all.html (7985 words)

	Automatic Groups
		Briefly, a finite state automaton uses an algorithmic method to determine whether objects called "words" have particular properties by looking at their components, called "letters." The automaton reads a word one letter at a time.
		After reading a letter, of which there are only a finite number, the automaton records that it is in a certain one of a finite number of "states." At any time, the only information the automaton knows is what state it is in.
		Since an automaton rejects or accepts words in a finite amount of time, whenever such an automaton exists, it is possible to solve the word problem.
	www.geom.uiuc.edu /docs/forum/automaticgroups/automaticgroups.html (1192 words)

	Finite State Automata
		A finite-state automaton is a device that can be in one of a finite number of states.
		An automaton is said to be start-useful iff every state is reachable from any of its initial states.
		An automaton is useful iff it is start-useful and for every state there is at least one final state reachable from that state.
	www.eti.pg.gda.pl /katedry/kiw/pracownicy/Jan.Daciuk/personal/thesis/node12.html (1437 words)

	Finite State Machines
		Finite automata are primarily used in parsing for recorgizing languages.
		One of the most important facts about finite automata is that instances of any regular expression can be recognized by a finite automaton.
		The notion of finite automata is mathematically rigorous.
	sakharov.net /fsmtutorial.html (913 words)

	Dr. Dobb's \| A Regular Expression Class Library \| May 1, 1998
		The finite automaton conducts a search by sequencing through a series of internal states while reading characters from the input string.
		The automaton jumps from one state to the next based on its current state and the character it receives from its input.
		This function feeds successive input characters to the automaton until it reaches the end of the input or an invalid state is reached.
	www.ddj.com /dept/cpp/184403496 (1432 words)

	Assignment 16 - Finite Automaton (Site not responding. Last check: )
		A finite automaton is an algorithm with a finite memory which scans through an input string or text.
		The finite memory is given by states, one of them being a starting state and several accepting states.
		The type of finite automata dealt with here is called deterministic since the function to compute the new state permits always only one unique value; otherwise the automaton would be called nondeterministic.
	www.comp.nus.edu.sg /~gem1501/assignment16.html (1553 words)

	Theory of Computation
		That an automaton may operate on a finite set of input data and end in a discernible final state motivates us to view the automaton as a mapping between the set of input symbols and its final state.
		Like a finite automaton, a Turing machine is a simple computing device consisting of a finite set of input states, finite set of input symbols, an initial state, and a transition function.
		Unlike a finite automaton, a Turing machine's input data is said to be given on a finite, but unbounded, strip of magnetic tape.
	www.theory.org /complexity/cdpt/html/node3.html (1966 words)

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