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| Â | Alan Turing |
 | | Probably Turing was aiming at the opposite idea, of finding a theory of the reduction process that would be predictive and computable, and so plug the gap in his hypothesis that the action of the brain is computable. | | | Turing's motivations were scientific rather than industrial or commercial, and he soon returned to the theoretical limitations of computation, this time focussing on the comparison of the power of computation and the power of the human brain. | | | Turing rapidly composed a detailed plan for a modern stored-program computer: that is, a computer in which data and instructions are stored and manipulated alike. |
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http://plato.stanford.edu/entries/turing
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| Â | Turing reduction - Encyclopedia Glossary Meaning Explanation Turing reduction |
| | More formally, a Turing reduction is a function computable by an oracle machine with an oracle for A. If such a reduction exists, then every algorithm for M immediately yields an algorithm for L, formed by inserting a "call" to that algorithm at each place where the oracle machine uses it. | | | In computational complexity theory, a Turing reduction from a problem A to a problem B is, intuitively, a reduction which easily solves B, assuming A is easy to solve. | | | Turing reductions are often subjected to additional resource restrictions, for example that the oracle machine runs in polynomial time or logarithmic space; see polynomial-time reduction and log-space reduction for details. |
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http://www.encyclopedia-glossary.com/en/Turing-reduction.html
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| Â | Alan Turing |
| | Probably Turing was aiming at the opposite idea, of finding a theory of the reduction process that would be predictive and computable, and so plug the gap in his hypothesis that the action of the brain is computable. | | | Turing's motivations were scientific rather than industrial or commercial, and he soon returned to the theoretical limitations of computation, this time focussing on the comparison of the power of computation and the power of the human brain. | | | Turing rapidly composed a detailed plan for a modern stored-program computer: that is, a computer in which data and instructions are stored and manipulated alike. |
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http://plato.stanford.edu/entries/turing
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| Â | URCS Theory Technical Reports |
| | These are Turing reductions in which the sequence of query lengths is nonincreasing (nondecreasing). | | | Despite the fact that we prove query-increasing and query-decreasing Turing reductions to in the general case be strictly weaker than Turing reductions, we identify a broad class of sets A for which any set that Turing reduces to A will also reduce to A via both query-increasing and query-decreasing Turing reductions. | | | Keywords: computational complexity; space complexity; probabilistic Turing machine; nodeterministic Turing machine; multihead finite automaton. |
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http://www.cs.rochester.edu/trs/theory-trs.html
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| Â | Alan Turing |
| | Probably Turing was aiming at the opposite idea, of finding a theory of the reduction process that would be predictive and computable, and so plug the gap in his hypothesis that the action of the brain is computable. | | | Turing's motivations were scientific rather than industrial or commercial, and he soon returned to the theoretical limitations of computation, this time focussing on the comparison of the power of computation and the power of the human brain. | | | Turing rapidly composed a detailed plan for a modern stored-program computer: that is, a computer in which data and instructions are stored and manipulated alike. |
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http://plato.stanford.edu/entries/turing
(9753 words)
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| Â | Polynomial-time Turing reduction |
| | In computational complexity theory a polynomial-time Turing reduction or Cook reduction of a decision problem L to a decision problem M is an oracle machine that has an oracle for M and can decide L in polynomial time. | | | Polynomial-time Turing reduction | | | It uses material from the wikipedia article Polynomial-time Turing reduction. |
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http://www.eurofreehost.com/po/Polynomial-time_Turing_reduction.html
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| Â | Polynomial-time reduction - Wikipedia, the free encyclopedia |
| | In computational complexity theory a polynomial-time reduction is a reduction which is computable by a deterministic Turing machine in polynomial time. | | | If it is a Turing reduction, it is called a polynomial-time Turing reduction or Cook reduction. | | | If it is a many-one reduction, it is called a polynomial-time many-one reduction, polynomial transformation, or Karp reduction. |
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http://en.wikipedia.org/wiki/Polynomial-time_reduction
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| Â | ipedia.com: Polynomial-time Turing reduction Article |
| | In computational complexity theory a polynomial-time Turing reduction or Cook reduction of a decision problem L to a decision problem M is an oracle machine that has an oracle for M and can decide L i... | | | In computational complexity theory a polynomial-time Turing reduction or Cook reduction of a decision problem L to a decision problem M is an oracle machine that has an oracle for M and can decide L in polynomial time. | | | Starware search is an excellent resource for quality sites on polynomial time turing reduction and much more! |
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http://www.ipedia.com/polynomial_time_turing_reduction.html
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| Â | The reduction Spot - accent , active noise , anxiety , arms , arms treaty, |
| | complete, Turing reduction, Cook reduction, Karp reduction, l-reduction, many-one reduction, polynomial-time reduction... | | | She large she orp rif sonic redution time reduction+ reduction, my theorem from debt new york reduce linear report employer. | | | The Crime Reduction Website provides community safety and crime prevention practitioners with information, statistics, guidance and training to reduce crime and anti-social behaviour in their... |
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http://andersonsampservice.com
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| Â | Polynomial-time reduction - Wikipedia, the free encyclopedia |
| | If it is a Turing reduction, it is called a polynomial-time Turing reduction or Cook reduction. | | | Cook reductions are more powerful than Karp reductions; for example, any problem in co-NP has a Cook reduction to a problem in NP. | | | Polynomial-time reductions are important and widely-used because they are powerful enough to perform many transformations between important problems, but still weak enough that polynomial-time reductions from problems in |
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http://en.wikipedia.org/wiki/Polynomial-time_Turing_reduction
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| Â | Randomized Turing Reductions |
| | If in a p-time (ap-time) randomized Turing reduction all queries can be generated at the beginning independent of other queries, then the reduction is called a p-time (ap-time) randomized truth-table reduction. | | | Other types of reductions such as truth-table reductions and Turing reductions can be similarly defined for distributional problems. | | | However, it is not known whether truth-table or Turing reductions can help identify additional average-case NP-complete problems encountered in practice. |
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http://www.uncg.edu/mat/avg/avgcomp/node17.html
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| Â | (Hemaspaandra E.) On the Power of Positive Turing Reductions |
| | Abstract: In the early 1980s, Selman's seminal work on positive Turing reductions showed that positive Turing reduction to NP yields no greater computational power than NP itself. | | | In particular, positive Turing reduction to DP already yields all (and only) sets Turing reducibility to NP. | | | (Hemaspaandra E.) On the Power of Positive Turing Reductions |
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http://www.jucs.org/jucs_5_12/on_the_power_of
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| Â | Polynomial-time reduction - Wikipedia, the free encyclopedia |
| | In computational complexity theory a polynomial-time reduction is a reduction which is computable by a deterministic Turing machine in polynomial time. | | | Within the class P, however, polynomial-time reductions are inappropriate, because any problem in P can be polynomial-time reduced (both many-one and Turing) to any other problem in P. Thus, for classes within P such as L, NL, NC, and P itself, log-space reductions are used instead. | | | Polynomial-time reductions are important and widely-used because they are powerful enough to perform many transformations between important problems, but still weak enough that polynomial-time reductions from problems in NP or co-NP to problems in P are considered unlikely to exist. |
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http://en.wikipedia.org/wiki/Polynomial-time_many-one_reduction
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| Â | Polynomial-time reduction - Wikipedia, the free encyclopedia |
| | In computational complexity theory a polynomial-time reduction is a reduction which is computable by a deterministic Turing machine in polynomial time. | | | Within the class P, however, polynomial-time reductions are inappropriate, because any problem in P can be polynomial-time reduced (both many-one and Turing) to any other problem in P. Thus, for classes within P such as L, NL, NC, and P itself, log-space reductions are used instead. | | | Polynomial-time reductions are important and widely-used because they are powerful enough to perform many transformations between important problems, but still weak enough that polynomial-time reductions from problems in NP or co-NP to problems in P are considered unlikely to exist. |
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http://en.wikipedia.org/wiki/Polynomial-time_many-one_reduction
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| Â Â |
| Â | Polynomial-time reduction - Wikipedia, the free encyclopedia |
| | In computational complexity theory a polynomial-time reduction is a reduction which is computable by a deterministic Turing machine in polynomial time. | | | Within the class P, however, polynomial-time reductions are inappropriate, because any problem in P can be polynomial-time reduced (both many-one and Turing) to any other problem in P. Thus, for classes within P such as L, NL, NC, and P itself, log-space reductions are used instead. | | | Polynomial-time reductions are important and widely-used because they are powerful enough to perform many transformations between important problems, but still weak enough that polynomial-time reductions from problems in NP or co-NP to problems in P are considered unlikely to exist. |
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http://en.wikipedia.org/wiki/Polynomial-time_reduction
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| Â | Cook reduction |
| | See also NP-complete, Turing reduction, Karp reduction, l-reduction, many-one reduction, polynomial-time reduction. | | | Definition: A reduction computed by a deterministic polynomial time oracle Turing machine. | | | HTML page formatted Wed Dec 22 09:35:02 1999. |
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http://www.guides.sk/CRCDict/HTML/cookreductin.html
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| Â | Re: page course Barcelona |
| | I will present the notions of polynomial functional reduction (Karp reduction) and of polynomial Turing reduction (Cook reduction). | | | I will also define the notions of functional reduction and of Turing reduction and the corresponding notions of complete problems. | | | I will present the famous halting problem and the classes R, RE and coRE of formal languages (encoding decision problems). |
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http://www.tecn.upf.es/~hgeffner/course04-pierre.html
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| Â | Polynomial-time reduction - Wikipedia, the free encyclopedia |
| | Within the class P, however, polynomial-time reductions are inappropriate, because any problem in P can be polynomial-time reduced (both many-one and Turing) to any other problem in P. Thus, for classes within P such as L, NL, NC, and P itself, log-space reductions are used instead. | | | In computational complexity theory a polynomial-time reduction is a reduction which is computable by a deterministic Turing machine in polynomial time. | | | Polynomial-time reductions are important and widely-used because they are powerful enough to perform many transformations between important problems, but still weak enough that polynomial-time reductions from problems in NP or co-NP to problems in P are considered unlikely to exist. |
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http://en.wikipedia.org/wiki/Polynomial-time_Turing_reduction
(278 words)
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| Â | Cook reduction |
| | See also NP-complete, Turing reduction, Karp reduction, l-reduction, many-one reduction, polynomial-time reduction. | | | Definition: A reduction computed by a deterministic polynomial time oracle Turing machine. | | | HTML page formatted Fri Dec 17 14:50:30 2004. |
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http://www.nist.gov/dads/HTML/cookreductin.html
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| Â | Randomized Turing Reductions |
| | It is a long-standing open problem whether Turing reductions (or truth-table reductions) are provably more powerful than many-one reductions on NP problems. | | | If in a p-time (ap-time) randomized Turing reduction all queries can be generated at the beginning independent of other queries, then the reduction is called a p-time (ap-time) randomized truth-table reduction. | | | We also note that Theorem 4.1 remains true if one uses deterministic Turing reductions [Gur91a]. |
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http://www.uncg.edu/mat/avg/avgcomp/node17.html
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| Â | Karp reduction |
| | See also NP-complete, Turing reduction, Cook reduction, l-reduction, many-one reduction, polynomial-time reduction. | | | Definition: A reduction given by a polynomial time computable transformation function. | | | Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "Karp reduction", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST. |
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http://www.itl.nist.gov/div897/sqg/dads/HTML/karpreductin.html
(114 words)
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| Â | Karp reduction |
| | See also NP-complete, Turing reduction, Cook reduction, l-reduction, many-one reduction, polynomial-time reduction. | | | Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "Karp reduction", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST. | | | Definition: A reduction given by a polynomial time computable transformation function. |
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http://www.nist.gov/dads/HTML/karpreductin.html
(114 words)
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| Â | Refutation of Alan Turing's argument of unsolvability of the Halting Problem |
| | This implies that any problem whose apparent unsolvability has been established by its reduction to the Halting Problem of Turing machines must be exonerated from the domain of formal disciplines. | | | Turing, Alan (1936-7), On computable numbers, with an application to the Entscheindugsproblem, edited by Davis, M. The Undecidable, Raven Press, New York. | | | If by Turing’s thesis each computable function by mechanical methods is computable by a Turing machine, and each computable function by a Turing machine is computable by mechanical methods, then cannot be reason field to outline any matter of uncomputability regarding the Turing machines, that is, regarding mechanical methods. |
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http://www.deducing.com/rott.html
(114 words)
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| Â | reduction |
| | See also NP-complete, Turing reduction, Cook reduction, Karp reduction, l-reduction, many-one reduction, polynomial-time reduction. | | | Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "reduction", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST. | | | Note: From Algorithms and Theory of Computation Handbook, page 24-19, Copyright © 1999 by CRC Press LLC. |
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http://www.nist.gov/dads/HTML/reduction.html
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| Â | lect01.tex |
| | There are two main types of reductions in Complexity Theory: \BI \item {\bf Turing reductions.} The most general type of reduction between problems (which works for relations) is of the following type (this is called a many-many reduction or Turing reduction). | | | \EI The problem with this kind of reduction is that it is hard to separate complexity classes using it. | | | In recent years the focus has mostly been on removing randomness from algorithms, or reductions. |
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http://theory.csail.mit.edu/%7Emadhu/ST05/scribe/lect01.tex
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| Â | Cook reduction |
| | Cook reduction of pi_1 to pi_2 is a Turing machine appropriate for... | | | A Karp reduction provides a Cook reduction, since a Turing machine could decide... | | | If a Cook reduction exists then pi_2 is in some sense "at least as hard" as pi_1, since a machine which solves pi_2 could be used to construct one which solves pi_1. |
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http://www.citidel.org/dlxml/oai_dc-oai:PlanetMath:CookReduction.xml
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| Â | Turing and Penrose: Andrew Hodges |
| | Turing's interest in reduction, and the lack of a rule for it, should not be confused with prospect of quantum computation as developed since the 1980s. | | | Turing here described the universal machine property, applying it to the brain, but said that its applicability required that the machine whose behaviour is to be imitated 'should be of the sort whose behaviour is in principle predictable by calculation. | | | Turing does not make this point, but the fact that he insisted on bringing this abstruse material into a popular radio broadcast shows he considered it of general importance, not a mathematician's private anxiety. |
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http://www.turing.org.uk/philosophy/lecture2.html
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| Â | Book review of Roger Penrose |
| | Subjective reduction is what happens when an observer measures a quantity in a quantum system: the system is not in any specific state (the system is in a "superposition" of possible states) until it is observed, the observation causes the system to reduce (or "collapse") to a specific state. | | | Somehow this relates to Goedel's theorem, which puts a limit to what a Turing machine can do, a limit that does not apply to the human mind; ergo a Turing machine cannot be a mind, and, viceversa, a mind is not a Turing machine. | | | Penrose is obsessed with that limit and is probably aware that all neurobiology is using brain models that are computationally equivalent to Turing machines (neurobiologists are happy to claim that they can simulate their models on a computer, but Penrose is happy to counter that this proves their model cannot be correct). |
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http://www.thymos.com/mind/penrose.html
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