Titlebook: Computation, Physics and Beyond; International Worksh Michael J. Dinneen,Bakhadyr Khoussainov,André Nies Book 2012 Springer-Verlag GmbH Ber

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BRAVE

Fundamentals of Topological Insulators, alone, a general invariance theorem is proved and sufficient conditions are stated for complexity to be computable. Next, universal functions are introduced, defined by pairing functions. It is shown that properties of the pairing functions, that is, of the joint encodings of functions and their in

单色

Constructing the Infimum of Two Projectionsn a constructive convergence proof for the algorithm, one must add some hypotheses such as Markov’s principle or the locatedness of a certain range; and that in the finite-dimensional case, the existence of both the infimum and the supremum of the two projections suffices for the convergence of the algorithm.

起来了

How Much Information Can There Be in a Real Number?lude and Dinneen attempting to compute Ω. Furthermore, we propose measuring human intellectual progress (not scientific progress) via the number of bits of Ω that can be determined at any given moment in time using the current mathematical theories.

六个才偏离

anchor

macrophage

Strong Interactions in Low DimensionsThe present paper generalises results by Tadaki [12] and Calude et al. [1] on oscillation-free partially random infinite strings. Moreover, it shows that oscillation-free partial Chaitin randomness can be separated from oscillation-free partial strong Martin-Löf randomness by .-definable sets of infinite strings.

fulcrum

Bounded RandomnessWe introduce some new variations of the notions of being Martin-Löf random where the tests are all clopen sets. We explore how these randomness notions relate to classical randomness notions and to degrees of unsolvability.

迅速成长

Hartmanis-Stearns Conjecture on Real Time and TranscendenceHartmanis-Stearns conjecture asserts that any number whose decimal expansion can be computed by a multitape Turing machine is either rational or transcendental. After half a century of active research by computer scientists and mathematicians the problem is still open but much more interesting than in 1965.

mechanical