Kolmogorov Complexity and Instance Complexity of Recursively Enumerable Sets
نویسندگان
چکیده
منابع مشابه
Kolmogorov Complexity and Instance Complexity of Recursively Enumerable Sets
We study in which way Kolmogorov complexity and instance complexity affect properties of r.e. sets. We show that the well-known 2 log n upper bound on the Kolmogorov complexity of initial segments of r.e. sets is optimal and characterize the T-degrees of r.e. sets which attain this bound. The main part of the paper is concerned with instance complexity of r.e. sets. We construct a nonrecursive ...
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We study the computably enumerable sets in terms of the: (a) Kolmogorov complexity of their initial segments; (b) Kolmogorov complexity of finite programs when they are used as oracles. We present an extended discussion of the existing research on this topic, along with recent developments and open problems. Besides this survey, our main original result is the following characterization of the ...
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The main purpose of this work is to characterize computably enumerable (c.e.) sets and generalized c.e. sets according to Kolmogorov complexity hierarchy. Given a set A, we consider A m, the initial segment of length m of the characteristic sequence of A. We show that the characteristic sequence of a 2 x-c.e. set can be random in the sense of Martin-LL of. We show that for x n-c.e. sets A, the ...
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TABLE OF CONTENTS Introduction Chapter I. The relation of the structure of an r.e. set to its degree. 1. Post's program and simple sets. 2. Dominating functions and quotient lattices. 3. Maximal sets and high degrees. 4. Low degrees, atomless sets, and invariant degree classes. 5. Incompleteness and completeness for noninvariant properties. Chapter II. The structure, automorphisms, and elementa...
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For given sets A, B, and Z of natural numbers where the members of Z are z0, z1, . . . in ascending order, one says that A is selected from B by Z if A(i) = B(zi) for all i. Furthermore, say that A is selected from B if A is selected from B by some recursively enumerable set, and that A is selected from B in n steps iff there are sets E0, E1, . . . , En such that E0 = A, En = B, and Ei is selec...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 1996
ISSN: 0097-5397,1095-7111
DOI: 10.1137/s0097539794268789