Zusammenfassung
Berechenbarkeit ist Ressourcen-und Logik -relativ. [COPELAND/SYLVAN 1999, 2000] — Orthodoxe prinzipielle Berechenbarkeitstheorie/Rekursionstheorie abstrahiert von Ressourcen an Raum und Zeit und ist mit formalen Limitationstheoremen konfrontiert. Praktische Berechenbarkeit andererseits bedeutet die Strukturprobleme der Komplexitätsklassen; eine Widerspenstigkeit des ‚Materials‘ mit einem Pandämonium an Effekten. — Das Verhältnis der beiden ist nicht trivial. TURING selbst formalisierte in SYSTEMS OF LOGIC BASED ON ORDINALS relative Berechenbarkeit als Orakel-Turingmaschinen. [TURING 1939:172–173] — Für zwei Mengen A, B ℕ, heißt A Turing-reduzierbar auf B, A ≤ T B, wenn es eine Orakelmaschine mit dem Orakel B gibt, welche die charakteristische Funktion von A berechnet.
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Literatur
AMBOS-SPIES, K., FEJER, P., (Unveröffentlicht): Degrees of Unsolvability. e-print: http://www.cs.umb.edu/~fejer/articles/History_of_Degrees.pdf
BAKER, T.P., GILL, J., SOLOVAY, R. (1975): Relativizations of the P =? NP Question. In: SIAM Journal on Computing 4,4: 431–442.
BENNETT, Ch.H., GILL, J., (1981): Relative to a Random Oracle A, P A != NP A != co-NP A with Probability 1. SIAM Journal on Computing 10(1): 96–113.
CANETTI, R. et al. (1998): The Random Oracle Methodology Revisited, STOC 1998: 209–218.
CHAITIN, G. J. (1987): Computing the Busy Beaver Function, In: T. M. Cover, B. Gopinath, Open Problems in Communication and Computation, Springer, 1987: 108–112.
CHANG et al. (1994): The Random Oracle Hypothesis is False. Journal of Computer and System Sciences 49 (1): 24–39.
COPELAND, J., PROUDFOOT, D. (1999): Alan Turing’s forgotten ideas in computer science. Scientific American April 1999.
COPELAND, B.J., SYLVAND, R. (1999): Beyond the universal Turing machine. Australasian Journal of Philosophy 77: 46–66.
COPELAND, B.J., SYLVAN, R. (2000): Computability is Logic-Relative. In: PRIEST, G., HYDE, D. (eds.): Sociative Logics and their Applications. London, Ashgate: 189–199.
COVER, T.M., (1973): On determining the irrationality of the mean of a random variable. Annals of Statistics 1 (5): 862–871
DAVIS, M. (2006): Why there is no such discipline as hypercomputation. Applied Mathematics and Computation, 178, 1,1: 4–7.
DAVIS, M. (2008): What is... Turing Reducibility? Notices American Mathematical Society 53, 10: 1218–1219.
DEUTSCH, D. (1985): Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer. Proceedings of the Royal Society, Series A, 400: 97–117.
EGAN, G. (1995): Permutation City. London: Millennium Orion.
FAGIN, R. (1974): Generalized first-order spectra and polynomial-time recognizable sets. In: KARP, R. (ed.) (1974): Complexity of Computation. SIAM-AMS Proceedings 7. Providence, American Mathematical Society: 27–41.
GOOD, I.J., (1970): The proton and neuron masses and a conjecture for the gravitational constant. Physical Review Letters 33A: 383–384.
HOPCROFT J.E., R. MOTWNI, J.D. ULLMAN, (22002): Einführung in die Automatentheorie, Formale Sprachen und Komplexitätstheorie. Springer.
JAPARIDZE, G. (1994): The logic of the arithmetical hierarchy. Annals of Pure and Applied Logic 66: 89–112.
LENZ, F., (1951): The ratio of proton and electron masses, Physical Review 82:554.
LESHEM, A. (2006): An experimental uncertainty implied by failure of the physical Church-Turing thesis. e-print: arXiv:math:ph/ 060417v1.
ODIFREDDI, P. (1989): Classical Recursion Theory. Amsterdam, North-Holland.
PAPADIMITRIOU, CH.H. (1994): Computational Complexity. Reading Mass., Addison Wesley Longman. Section 14.3: Oracles: 339–343.
RADÓ, T. (1962): On noncomputable function., Bell Systems Tech. J. 41, 3: 877–884.
ROGERS Jr. H., (1967): Theory of Recursive Functions and Effective Computability. McGraw-Hill, 1967. Nachdruck bei MIT-Press, Cambridge 1987.
ROSENTHAL, J. S., (2006): A first look at rigorous probability theory. World Scientific Publishing, Hackensack.
SHORE, R.A.; SLAMAN, T.A. (1999): Defining the Turing jump. Math. Res. Lett. 6 (5–6): 711–722. Retrieved 2008-07-13.
SHOENFIELD, J., (1993): Recursion theory, Lecture Notes in Logic 1. Springer Verlag.
SIPSER, M. (1997): Introduction to the Theory of Computation. Boston, PWS Publishing Company, Section 9, 2: Relativisation: 318-321.
SOARE, R., (1987): Recursively enumerable sets and degrees: a study of computable functions and computable generated sets. Springer-Verlag.
S tannett, M., (2006), The case for hypercomputation. Applied Mathematics and Computation, Volume 178, Issue 1, 1: 8–24.
TURING, A. (1936/37): On Computable Numbers, with an Application to the Entscheidungsproblem. In: Proceedings of the London Mathematical Society 2, 42: 230–265.
TURING, A. (1939): Systems of logic based on ordinals, In: Proceedings of the London Mathematical Society 2, 45: 161–228; Reprinted in: DAVIS, M. (ed.) (1965, 2004): The Undecidable. Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. Raven Press, New York.
WYLER, A., (1971): A mathematicians version of the fine stucture constant. Physics Today 24: 17–19.
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Putzmann, L.M. (2010). Orakel. In: Trogemann, G. (eds) Code und Material Exkursionen ins Undingliche. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0121-6_10
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