Machine dependence of degrees of difficulty
نویسندگان
چکیده
منابع مشابه
A. Machine Dependence of Degrees of Difficulty
One may define a degree-of-difficulty relation for total recursive functions by saying that f g (f is at least as difficult as g) if to each program for computing f there corresponds a program for computing g such that g(x) takes no more steps to compute than f(x) for almost all x. Unfortunately, such an ordering is highly dependent on our choice of mathematical model for a computer (cf. Hartma...
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Important examples of Π1 classes of functions f ∈ ω are the classes of sets (elements of 2) which separate a given pair of disjoint r.e. sets: S2(A0, A1) := { f ∈ 2 : (∀i < 2)(∀x ∈ Ai)f(x) 6= i }. A wider class consists of the classes of functions f ∈ k which in a generalized sense separate a k-tuple of r.e. sets (not necessarily pairwise disjoint) for each k ∈ ω: Sk(A0, . . . , Ak−1) := { f ∈ ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1965
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1965-0181538-0