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Topic: Alternating Turing machine

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	Alternating Turing machine - Wikipedia, the free encyclopedia
		In computational complexity theory, an alternating Turing machine (ATM) is a non-deterministic Turing machine (NTM) with a rule for accepting computations that generalizes the rules used in the definition of the complexity classes NP and co-NP.
		Perhaps the simplest problem for alternating machines to solve is the quantified boolean formula problem, which is a generalization of the boolean satisfiability problem in which each variable can be bound by either an existential or a universal quantifier.
		The alternating machine branches existentially to try all possible values of an existentially quantified variable and universally to try all possible values of a universally quantified variable, in the left-to-right order in which they are bound.
	en.wikipedia.org /wiki/Alternating_Turing_machine (971 words)

	Computational Complexity: Favorite Theorems: Alternation
		An alternating Turing machine is a nondeterministic machine with states marked either existential or universal.
		Alternation causes a shift in the time-space hierarchy of classes: P = AL, PSPACE = AP, EXP = APSPACE, EXPSPACE = AEXP, etc. More importantly the two fundamental resource bounds of time and space are really just the same concept on different models.
		Also alternating machines set the stage for interactive proof systems which led to probabilistically checkable proofs, perhaps the most productive line of research in complexity over the past fifteen years.
	weblog.fortnow.com /2006/02/favorite-theorems-alternation.html (311 words)

	zambetti.com - turing
		Turing is an interactive graphical embodiment of an abstract computational model developed by Alan Turing.
		The turing machine space is organized in a tripartite structure to the right of the control panel.
		The output of the machine is communicated by the set of colored rectangles on the tape when the machine halts.
	www.zambetti.com /projects/turing (2091 words)

	Turing Machines (Site not responding. Last check: 2007-11-07)
		The Turning machine was proposed to formalize the intuitive notion of an algorithm by Alan Turing in 1936.
		A Universal Turing Machine is then a Turing machine that has on its input tape a definition of some Turing machine and a string.
		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 /~cs_dept/KU/Logic/turingMachine.html (881 words)

	Abstracts
		The alternating turing machine is used to characterize the polynomial hierarchy.
		We show, that each level of the hierarchy with alternating pushdown automata is included in the corresponding level of the oracle hierarchy and that the logarithmic closure over both levels is the corresponding level of the polynomial hierarchy with one alternation less.
		Hereby we prove, that the hierarchy with alternating context-free grammars is identical with the oracle hierarchy over the context-free languages and that in case of unbounded alternation context-free and context-sensitive grammars have the same power.
	www-fs.informatik.uni-tuebingen.de /~reinhard/abstracts.html (3970 words)

	Not Natural Ona Turing Machine
		Could of course be done with a Turing machine running the GameOfLife with NAND gates constructing a computer that computes the control logic.
		First off, the Turing Machine could just as easily have atomic compareandswap as atomic read/write, so that's comparing apples and oranges; the simple Turing machines are all sequential, not parallel, anyway, so a purely sequential Turing machine everything or nothing "atomic" depending on how you look at it.
		You're forgetting that the point has never been that Turing Machines are identical to all other computational devices, merely that they are computational equivalent in power, typically proved by simulating the other device.
	c2.com /cgi/wiki?NotNaturalOnaTuringMachine (1585 words)

	Viliam Geffert - Abstracts
		Abstract: We shall show that for each $s(n)$-space-bounded nondeterministic Turing machine recognizing a language $L{\subseteq}1^$ there exists an equivalent deterministic $O(s^2(n))$-space-bounded machine, and also a nondeterministic $O(s(n))$-space-bounded machine* recognizing the complement of $L$, for any $s(n)$, independent of whether $s(n)$ is below $\log(n)$ or space constructible.
		Abstract: The complexity measure under consideration is SPACE $\times$ REVERSALS for Turing machines that are able to branch both existentially and universally.
		We show that, though the underlying machine for the synchronized alternation is alternating, the nature of message broadcasting is nondeterministic.
	kosice.upjs.sk /~kmi/Geffert/Gefww3.htm (1374 words)

	[No title]
		We discussed the notion of a problem and its input and output encodings and, independently, definitions and capabilities of machines in terms of memory usage and access, nondeterminism, alternation, randomization or simply deterministic execution.
		It is worthwhile considering problems where we wish to reverse the acceptance criterion, thereby designing a machine M' that accepts the complement language L' of the language L accepted by a machine M. We consider S(n) (S(n)>= log n) space-bounded machines M and their accepted languages for inputs of length n.
		This diagonalization argument is feasible for every S1(n)-space bounded machine, irrespective of its number t of tape symbols; if there are t tape symbols, M_w will require at most log t times S1(n) space, which is indeed dominated by S2(n) inspite of arbitrary choice of t, by choosing a sufficiently long w of length n.
	www.angelfire.com /or/sudebkumar/cc2005.html (1420 words)

	CMPSCI 601 Solutions to Final Exam, Summer 2003
		Question 2 (15): Let M be a one-tape Turing machine that always halts within some polynomial time bound p(n) on input of size n.
		The contents and possible head presence and machine state of this cell and this time are represented by O(1) circuit gates.
		By the Alternation Theorem, such an ATM exists iff G is in the class PSPACE.
	www.cs.umass.edu /~barring/cs601sum03/exam/finsol.html (1026 words)

	Turing machine (Site not responding. Last check: 2007-11-07)
		Definition: A model of computation consisting of a finite state machine controller, a read-write head, and an unbounded sequential tape.
		Depending on the current state and symbol read on the tape, the machine can change its state and move the head to the left or right.
		Unless otherwise specified, a Turing machine is deterministic.
	www.nist.gov /dads/HTML/turingMachine.html (196 words)

	[No title]
		example: parallel time of vector machine is equivalent to sequential space.
		ATM (S(n), T(n)): Language accepted by ATM with space S(n), time T(n).
		Theorem: ATM (logn, (logn)k) = NCk ¡V6¨f ª,/ öóSH¨$NC-algorithm and P-complete problems¨íLet f be a function Input: input of f Output: compute f NC1 reducible from f to g: using oracles of g, we can construct NC1 circuits computing f.
	www.cse.msu.edu /~cse838/Theory.ppt (614 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		In quest of Turing and Tarski, he arrived at Cornell where he gleaned much from the vast storehouse of Knowledge he discovered (notwithstanding occasional disturbing diversions when it seemed doubtful if he was pursuing the higher quests in the spheres of Computer Science or in Tennis and Cooking!).
		We describe an alternating Turing machine algoritlim to decide sentences of the theory of p-adically-closed fields.
		First we gave an alternating exponential time algorithm for deciding linear sentences in the theory of p-adically closed fields This also translates into a de- terministic algorithm running in exponential space or double exponential time.
	historical.ncstrl.org /tr/temp/ocr/cs-tr.cs.cornell.edu/TR92-1301 (16166 words)

	QIP abstracts
		In the general case a particular (nonzero) parametrisation is inferred, and its properties discussed in comparison with the literature on tunnelling times for both wavepackets and internal clocks.
		In Feynman9s path integral, the kernels are partially ordered over time (different alternate paths acting concurrently at the same time) and multiplied.
		This class of languages is accepted by polynomial space bounded deterministic Turing machine (or in PSPACE) which is the class solvable by an ATM in polynomial time.
	www.physics.adelaide.edu.au /itp/workshops/qip/qipabst2.html (2892 words)

	alternating Turing machine (Site not responding. Last check: 2007-11-07)
		Definition: A nondeterministic Turing machine having universal states, from which the machine accepts only if all possible moves out of that state lead to acceptance.
		See also model of computation, nondeterministic Turing machine, oracle Turing machine, probabilistic Turing machine, universal Turing machine.
		Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "alternating Turing machine", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/alternatngTr.html (141 words)

	probabilistic Turing machine (Site not responding. Last check: 2007-11-07)
		Definition: A Turing machine in which some transitions are random choices among finitely many alternatives.
		See also alternating Turing machine, nondeterministic Turing machine, oracle Turing machine, universal Turing machine, NP, RP, ZPP, BPP.
		Note: The typical, deterministic Turing machine (TM) can be seen as a probabilistic TM with no more than one alternative for each transition.
	www.nist.gov /dads/HTML/probablturng.html (164 words)

	Computational Complexity: February 2006
		The previous theoretician to receive the award was Shafi Goldwasser in 1996 and before that Donald Knuth in 1971.
		Peter Naur won the Turing Award (the closest CS has to a Nobel Prize) for his work on Algol 60.
		At New York's Kennedy airport today, an individual later discovered to be a public school teacher was arrested trying to board a flight while in possession of a ruler, a protractor, a compass, a slide rule, and a calculator.
	weblog.fortnow.com /archive/2006_02_01_archive.html (3885 words)

	universal Turing machine (Site not responding. Last check: 2007-11-07)
		Definition: A Turing machine that is capable of simulating any other Turing machine by encoding the latter.
		See also alternating Turing machine, nondeterministic Turing machine, oracle Turing machine, probabilistic Turing machine.
		Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "universal Turing machine", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
	www.darkridge.com /~jpr5/archive/dads/HTML/universalTur.html (125 words)

	Footnotes
		One can use one's favorite distributions to select it, e.g., one may select states and transition functions according to different distributions.
		For example, the linear speed-up theorem that holds for multi-tape Turing machines does not hold for some other models [Jon93].
		has been used as an intermediate time bound for an alternating Turing machine, to show that nondeterministic linear time is strictly more powerful than deterministic linear time [PPST83].So it would be interesting to extend log-exp functions to include functions like
	www.uncg.edu /mat/avg/avgcomp/footnode.html (266 words)

	Information and Computation Bibliography (Site not responding. Last check: 2007-11-07)
		Parallel random access machines with both multiplication and shifts.
		We prove that the class of languages accepted in polynomial time by Parallel Random Access Machines with both multiplication and shifts using exponentially many processors (PRAM[,\uparrow,\downarrow]-PTIME) includes the class of languages accepted in exponential time and polynomial alternations* by an alternating Turing machine and is included in
		It follows that the class of languages accepted by a PRAM[*,\uparrow,\downarrow] in logarithmic time (using polynomially many processors) includes the polynomial hierarchy and is included in
	theory.lcs.mit.edu /~iandc/References/trahanrl1994:96.html (211 words)

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