Kleene's Amazing Second Recursion Theorem
نویسنده
چکیده
Part 1. Self-reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. Self reproducing Turing machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2. Myhill’s characterization of r.e.-complete sets . . . . . . . . . . . . . . . . . . . . . . . . . 5 3. The Myhill-Shepherdson Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1. Aside: the two recursion theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4. The Kreisel-Lacombe-Shoenfield-Ceitin Theorem. . . . . . . . . . . . . . . . . . . . . 9 5. Incompleteness and undecidability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6. Solovay’s theorem in provability logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
منابع مشابه
Kleene ’ s Amazing Second Recursion Theorem Extended
Kleene states the theorem with V = N, relative to specific φ, S n , supplied by his Enumeration Theorem, m = 0 (no parameters ~y) and n ≥ 1, i.e., not allowing nullary partial functions. And most of the time, this is all we need; but there are a few important applications where choosing “the right” φ, S n , restricting the values to a proper V ( N or allowing m > 0 or n = 0 simplifies the proof...
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We study computer virology from an abstract point of view. Viruses and worms are self-replicating programs, whose definitions are based on Kleene’s second recursion theorem. We introduce a notion of delayed recursion that we apply to both Kleene’s second recursion theorem and Smullyan’s double recursion theorem. This leads us to define four classes of viruses, two of them being polymorphic. The...
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Kleene's Second Recursion Theorem provides a means for transforming any program p into a program e(p) which rst creates a quiescent self copy and then runs p on that self copy together with any externally given input. e(p), in eeect, has complete (low level) self knowledge, and p represents how e(p) uses its self knowledge (and its knowledge of the external world). Innnite regress is not requir...
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تاریخ انتشار 2009