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	Turing machine - Wikipedia, the free encyclopedia
		The thesis that states that Turing machines indeed capture the informal notion of effective or mechanical method in logic and mathematics is known as the Church-Turing thesis.
		Turing machines shouldn't be confused with the Turing test, Turing's attempt to capture the notion of artificial intelligence.
		The concept of a Turing machine was used as an educational tool in the science fiction novel The Diamond Age (1995), by Neal Stephenson.
	en.wikipedia.org /wiki/Turing_machine (2318 words)

	Probabilistic Turing machine - Wikipedia, the free encyclopedia
		In computability theory, a probabilistic Turing machine is a non-deterministic Turing machine which randomly chooses between the available transitions at each point with equal probability.
		As a consequence, a probabilistic Turing machine can (unlike a deterministic Turing Machine) have stochastic results; on a given input and instruction state machine, it may have different run times, or it may not halt at all; further, it may accept an input in one execution and reject the same input in another execution.
		Probabilistic computation is also critical for the definition of most classes of interactive proof systems, in which the verifier machine depends on randomness to avoid being predicted and tricked by the all-powerful prover machine.
	en.wikipedia.org /wiki/Probabilistic_Turing_machine (395 words)

	Probabilistic Turing Machine: Definition and Links by Encyclopedian.com - All about Probabilistic Turing Machine
		A probabililstic Turing machine, in computability theory, is equivalent to a Turing machine except that it has an additional instruction that allows it to randomly choose an execution path.
		As a consequence, a probabalistic Turing machine can (unlike a Turing Machine) have stochastic results; on a given input and instruction state machine, it may have different run times, or it may not halt at all.
		A non-deterministic Turing machine is like a probablistic one, except it guesses the correct answer (if that applies) every time.
	www.encyclopedian.com /pr/Probabilistic-Turing-Machine.html (177 words)

	PlanetMath: Turing machine (Site not responding. Last check: 2007-10-21)
		The machine has a finite set of states, and with every move the machine can change states, change the symbol written on the current cell, and move one space left or right.
		A Turing machine may be viewed as computing either a partial function or a relation.
		An equivalent definition is that there is a Turing machine which halts in an accepting state only on members of the relation and always halts.
	planetmath.org /encyclopedia/TuringMachine2.html (748 words)

	Knowledge King - Probabilistic Turing machine (Site not responding. Last check: 2007-10-21)
		A probabilistic Turing machine, in computability theory, is equivalent to a Turing machine except that it has an additional instruction that allows it to randomly choose an execution path.
		As a consequence, a probabilistic Turing machine can (unlike a Turing Machine) have stochastic results; on a given input and instruction state machine, it may have different run times, or it may not halt at all.
		A non-deterministic Turing machine is like a probabilistic one, except it guesses the correct answer (if that applies) every time.
	www.knowledgeking.net /encyclopedia/p/pr/probabilistic_turing_machine.html (156 words)

	Turing Machine [Definition] (Site not responding. Last check: 2007-10-21)
		The Turing machine is an abstract machine introduced in 1936 by Alan TuringAlan Mathison Turing (June 23, 1912–June 7, 1954) was a British mathematician, logician, cryptographer, and war hero, and is widely considered to be the father of computer science.
		The concept of a Turing machine was used as an educational tool in the science fictionScience fiction is a form of speculative fiction principally dealing with the impact of imagined science and technology, or both, upon society and persons as individuals.
		Probabilistic Turing machineIn computability theory, a probabilistic Turing machine is a non-deterministic Turing machine which randomly chooses between the available transitions at each point with equal probability.
	www.wikimirror.com /Turing_machine (2831 words)

	[No title]
		Each computation of a probabilistic Turing transducer is similar to that of a nondeterministic Turing transducer, the only exception arising upon reaching a configuration from which more than one move is possible.
		Probabilistic Turing machines are defined similarly to probabilistic Turing transducers.
		The probabilistic Turing machine in the following example is, in essence, a probabilistic pushdown automaton that accepts a non-context-free language.
	www.cse.ohio-state.edu /~gurari/theory-bk/theory-bk-sixse3.html (935 words)

	Encyclopedia: Probabilistic Turing Machine (Site not responding. Last check: 2007-10-21)
		In theoretical computer science, an ordinary (deterministic) Turing machine (DTM) has a transition rule that specifies for a given current state of the head and computer (s,q) a single instruction (s, q, d), where s is the symbol to be written by the head, q is the subsequent state...
		In complexity theory, ZPP (Zero-error Probabilistic Polynomial time) is the set of problems for which a probabilistic Turing machine exists with these properties: It always returns the correct YES or NO answer.
		In computational complexity theory, RLP is the complexity class of problems solvable in logarithmithic space and polynomial time with probabilistic Turing machines that never accept incorrectly but are allowed to reject incorrectly less than 1/3 of the time; this is called one-sided error.
	www.nationmaster.com /encyclopedia/Probabilistic-Turing-Machine (816 words)

	Turing Machine (Site not responding. Last check: 2007-10-21)
		This behavior is completely determined by three parameters: (1) the state the machine is in, (2) the number on the square it is scanning, and (3) a table of instructions.
		Also, a ‘probabilistic automaton’ can be defined as a Turing machine in which the transition from input and state to output and state takes place with a certain probability (E.g.
		Turing machines were first proposed by Alan Turing, in an attempt to give a mathematically precise definition of "algorithm" or "mechanical procedure".
	www.science.uva.nl /~seop/archives/fall2000/entries/turing-machine (511 words)

	Philosophy of Mind Notes
		Turing machines are pretty much a mechanical box with a strip of tape running through them.
		A probabilistic Turing machine is one that is not guaranteed to go from one specific internal state to only one internal state.
		As the machine operates, from moment to moment, the odds determine which regular Turing machine the probabilistic Turing machine turns out to be.
	publish.uwo.ca /~dgault/phil20/mindnotes.htm (3887 words)

	Turing Soup - Monod
		In the abstract Turing machine model of computer execution and storage, a tape is read and modified by a head according to the state and the instructions stored in an action table on the machine.
		Machines can be equipped with matching elements that match with other matching elements on other machines in order to affect both matchines' internal state.
		As with traditional Turing machines, there are different ways to define the specification of a machine in the Monod model: through an actual state table or through a program in a suitable language, for instance.
	monod.sourceforge.net /manualhtml/Turing-Soup.html (1667 words)

	Randomized algorithm - Wikipedia, the free encyclopedia
		In common practice, this means that the machine implementing the algorithm has access to a pseudo-random number generator.
		Also refer to Probabilistic analysis, which is based on assuming something about the set of all possible inputs.
		The most basic randomized complexity class is RP, which is the class of decision problems for which there is an efficient (polynomial time) randomized algorithm (or probabilistic Turing machine) which recognizes NO-instances with absolute certainty and recognizes YES-instances with a probability of at least 1/2.
	en.wikipedia.org /wiki/Probabilistic_algorithm (1245 words)

	The generalized automaton and Turing's machine (from automata theory) -- Encyclopædia Britannica
		Turing originally conceived the machine as a mathematical tool that could infallibly recognize undecidable propositions—i.e., those mathematical statements that, within a given formal axiom system, cannot be shown to be either true or false.
		Turing, Alan M. When a play based on the life of British mathematician Alan Turing was staged in 1986, its title was ‘Breaking the Code'.
		A machine may be as simple as a screw, or it may be as large and complex as an automobile.
	www.britannica.com /eb/article-21501?tocId=21501 (832 words)

	The Turing Machine
		The Turing Machine concept was first introduced in Turing’s 1937 paper as a rigorous means of defining the concept of a 'definite method' or algorithm.
		Turing himself argued that the computational ability of the Turing Machine was equivalent to what could be achieved by the human brain.
		Turing himself wrote on this in a 1950 paper that is considered by many to be the birth of the field of AI.
	www.mohomed.com /iqbal/writing.html (3114 words)

	Read about Probabilistic Turing machine at WorldVillage Encyclopedia. Research Probabilistic Turing machine and learn ... (Site not responding. Last check: 2007-10-21)
		non-deterministic Turing machine which randomly chooses between the available transitions at each point with equal probability.
		Turing machine having an additional "write" instruction where the value of the write is
		uniformly distributed in the Turing Machine's alphabet (generally, an equal likelihood of writing a '1' or a '0' on to the tape.)
	encyclopedia.worldvillage.com /s/b/Probabilistic_Turing_Machine (245 words)

	Intelligent Design (Site not responding. Last check: 2007-10-21)
		In this context, t(a) is used to mean that the Turing machine generates a.
		Both the λ-calculus (devised by Alonzo Church) and the Turing machine capture this intuitive notion of an algorithm.
		A Quantum Turing Machine, as defined by Bernstein and Vazirani, is a triplet (Sigma, Q, delta), where Sigma is a finite alphabet with an identified blank symbol #, Q is a finite set of states with an identified initial state q
	cs.wwc.edu /~aabyan/Colloquia/TM.html (1585 words)

	Generation5 Forum - Turing-Machine computation
		It is my contention that the plausibility of Turing's account as an analysis of the computational capacities of physical machines rests upon a number of highly problematic assumptions whose plausibility in turn is grounded in the formalist stance towards mathematics.
		Turing machine functions or programs that can be run on Turing machines- in the millions and non-Turing machine functions that can be run on non-Turing machines zip point ding.
		It is certainly possible to speculate on the possibility of machines capable of performing operations beyond the capabilities of machines using Turing machine functions, but such speculation remains in the realm of science fiction until it can be demonstrated such machines can actually be built.
	www.generation5.org /forums/topic.asp?TOPIC_ID=463&whichpage=2 (6415 words)

	Quantum Turing Machine (Site not responding. Last check: 2007-10-21)
		The original Turing machine was deterministic (DTM): the head would be always in a single state, which would uniquely determine which direction it would go into and how far.
		A machine like that is called a probabilistic Turing machine (PTM), and it turns out that it is more powerful than the deterministic Turing machine in the sense that anything computable with DTM is also computable with PTM and usually faster.
		In particular in place of the Turing cell on the tape, that could hold either 0 or 1, in quantum Turing machine there is a qubit, which can hold a quantum superposition of 0 and 1.
	beige.ucs.indiana.edu /B679/node25.html (1164 words)

	ZPL - Wikipedia, the free encyclopedia
		In complexity theory, ZPL (Zero-error Probabilistic Logarithmic space) is the set of problems solvable by a probabilistic Turing machine which always yields the correct answer and uses logarithmic space on average.
		Probabilistic algorithms that always give the correct answer are called Las Vegas algorithms.
		A surprising result is that ZPL is equal to both RL and NL; thus, if a problem can be solved in logarithmic space with nondeterminism or with one-sided error, it can be solved with no error and logarithmic space on average.
	www.wikipedia.org /wiki/ZPL (131 words)

	[No title]
		As in the case of deterministic and nondeterministic Turing transducers, each move of a probabilistic Turing transducer is assumed to take one unit of time.
		A probabilistic Turing transducer M is said to be T(n) time-bounded, or of time complexity T(n), if M halts within T(n) time in each computation on each input of length n.
		The tractability of problems with respect to probabilistic time is determined by the existence of bounded-error probabilistic Turing transducers of polynomial time complexity for solving the problems.
	www.cse.ohio-state.edu /~gurari/theory-bk/theory-bk-sixse4.html (891 words)

	Nat' Academies Press, Probability and Algorithms (1992)
		This is a Turing machine that has an extra "random" tape containing a random string of zeros and ones that can be read as necessary.
		A probabilistic polynomial-time Turing machine (PPTM) is such a machine equipped with a clock that, when given an input of n bits, always halts after p(n) steps, where p is a fixed polynomial.
		The performance of such machines is averaged over the uniform distribution of all random bits read by the machine.
	www.nap.edu /books/0309047765/html/40.html (584 words)

	BPP - the free encyclopedia (Site not responding. Last check: 2007-10-21)
		In complexity theory,BPP is the class of decision problems solvable by a probabilistic Turing machine inpolynomial time, with an error probability of at most 1/3 for allinstances.
		BPP is one of the largest practical classes ofproblems, meaning most problems of interest in BPP have efficientprobabilistic algorithms that can berun quickly on real modern machines, by the method described above.For this reason it is of great practical interest which problemsand classes of problems are inside BPP.
		This class is defined for an ordinary Turing machineplus a source of randomness.
	www.encyclopedia-of-knowledge.com /?t=Bpp (355 words)

	ZPP - Open Encyclopedia (Site not responding. Last check: 2007-10-21)
		In complexity theory, ZPP (Zero-error Probabilistic Polynomial time) is the set of problems for which a probabilistic Turing machine exists with these properties:
		Alternatively, ZPP can be defined as the class of problems or which a probabilistic Turing machine exists with these properties:
		The definition of ZPP is based on probabilistic Turing machines.
	open-encyclopedia.com /ZPP (225 words)

	Turing machine (Site not responding. Last check: 2007-10-21)
		Definition: A model of computation consisting of a finite state machine controller, a read-write head, and an unbounded sequential tape.
		Unless otherwise specified, a Turing machine is deterministic.
		Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "Turing machine", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
	www.nist.gov /dads/HTML/turingMachine.html (190 words)

	SICOMP Volume 6 Issue 4
		A probabilistic Turing machine is a Turing machine with the ability to make decisions based on the outcomes of unbiased coin tosses.
		The partial function computed by a probabilistic machine is defined by assigning to each input the output which occurs with probability greater than $\frac{1}{2}$.
		It is shown that every nondeterministic machine can be simulated in the same space by a probabilistic machine with small error probability.
	locus.siam.org /SICOMP/volume-06/art_0206049.html (186 words)

	Articles - Church–Turing thesis (Site not responding. Last check: 2007-10-21)
		Any computer program can be translated into a Turing machine, and any Turing machine can be translated into any general-purpose programming language, so the thesis is equivalent to saying that any general-purpose programming language is sufficient to express any algorithm.
		When hearing of Church's proposal, Turing was quickly able to show that his Turing machines in fact describe the same set of functions (Turing 1936, 263ff).
		The universe is not a Turing machine (ie, the laws of physics are not Turing-computable), but incomputable physical events are not "harnessable" for the construction of a hypercomputer.
	gaple.com /articles/Church-Turing_thesis?mySession=ff70f147c8c688e41... (1195 words)

	Probabilistic Turing machine -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		In (Click link for more info and facts about computability theory) computability theory, a probabilistic Turing machine is a (Click link for more info and facts about non-deterministic Turing machine) non-deterministic Turing machine which randomly chooses between the available transitions at each point with equal probability.
		If we restrict the machine to logarithmic space instead of polynomial time, we obtain the analogous (Click link for more info and facts about RL) RL, Co-RL, (Click link for more info and facts about BPL) BPL, and (Click link for more info and facts about ZPL) ZPL.
		A (Click link for more info and facts about quantum computer) quantum computer is another model of computation that is inherently probabilistic.
	www.absoluteastronomy.com /encyclopedia/P/Pr/Probabilistic_Turing_machine.htm (288 words)

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