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[Kenta.blogspot.com] Ken's blog: Oracles: I wrote up above that in decideability analysis, one isn't trying to construct an oracle, but in cryptography, people are trying to construct random oracles, i.e, hash functions Whereas it's known that you will never have a hash function that will perform as well as the God-in-a-box described above, functions (algorithms) such as SHA-512 in the SHA-2 family and Whirlpool are thought to approximate it fairly well, and are quickly computable, and most importantly do not require infinite memory, in fact, they require no persistent memory at all between successive calls. (I say "are thought" as some people think hash functions still have a long way to get better.)

[Courseblog.cs.princeton.edu] The Computational Universe » DSR:             The ability for Turing to expose the existence of problems that are unsolvable create such difficult issues for Turing machines.  Some problems that may be thought to be solvable if enough time is allocated may actually be unsolvable for the Turing machines, which are given an infinite amount of time to complete a function.  Despite the importance of this characteristic of infinite time to complete a problem it creates issues.  And while the only reason a function would not be Turing-computable is due to it not having the technological ability to do so and not time.  The ability for the Turing machine to have infinite time lends itself to the problem of not being able to complete a function but individuals not knowing it cannot do to the infinite time allotted to Turing machines to do so.  So in many ways an unanswerable problem is created when a Turing machine is working on a particularly long or difficult problem. 

 [Vetta.org] vetta project: It includes Turing's paper on the computability of numbers, Shannon inventing information theory, and Rivest, Shamir and Adelman putting forward the RSA public-private key encryption system. In each case the paper is totally rubbished by the reviewer.

 [Nicksresearch.wordpress.com] Nick’s Research Blog: Proof outline: Suppose f describes the behaviour of a Turing machine M. That is, with p a sequence of bits, and where M's inputs are successive bits of p, f(p) is everything M outputs until M asks for more bits that p has (if that ever happens).

 [Logicomp.blogspot.com] Logicomp: January 2006: Anthony Widjaja To's Blog on Logic and ...: [I will have to confess many proofs about the 0-1 law, including Fagin's proof of the above theorem, are usually of great beauty.] Well, a primary concern of finite model theory is to determine how expressive a logic is over a given class of finite structures. By proving that a logic admits the 0-1 law, we show that any property whose asymptotic probability does not converge to either 0 or 1 is not expressible in the logic.

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