Kolmogorov numberings and minimal identification
نویسندگان
چکیده
منابع مشابه
Kolmogorov numberings and minimal identification
Identification of programs for computable functions from their graphs by algorithmic devices is a well studied problem in learning theory. Freivalds and Chen consider identification of ‘minimal’ and ‘nearly minimal’ programs for functions from their graphs. To address certain problems in minimal identification for Gödel numberings, Freivalds later considered minimal identification in Kolmogorov...
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Identification of programs for computable functions from their graphs by algorithmic devices is a well studied problem in learning theory. Freivalds and Chen consider identification of ‘minimal’ and ‘nearly minimal’ programs for functions from their graphs. Freivalds showed that there exists a Gödel numbering in which only finite classes of functions can be identified using minimal programs. To...
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In [3], Rogers discussed the concept of Gödel numbering. He defined a semi-effective numbering, constructed a semi-lattice of equivalence classes of semi-effective numberings, and showed that all Gödel numberings belong to the unique maximal element of this semi-lattice. In [l], Friedberg gave a recursive enumeration without repetition of the set of partial recursive functions of a single varia...
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We prove various results on effective numberings and Friedberg numberings of families related to algorithmic randomness. The family of all Martin-Löf random left-computably enumerable reals has a Friedberg numbering, as does the family of all Π 1 classes of positive measure. On the other hand, the Π 1 classes contained in the Martin-Löf random reals do not even have an effective numbering, nor ...
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This paper studies the Turing degrees of various properties defined for universal numberings, that is, for numberings which list all partial-recursive functions. In particular properties relating to the domain of the corresponding functions are investigated like the set DEQ of all pairs of indices of functions with the same domain, the set DMIN of all minimal indices of sets and DMIN∗ of all in...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1997
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(96)00295-2